2024 Trigonometric ratios

Key Terms. Trigonometric Ratios: ratios that relate the lengths of the sides of right triangles to their interior angles. Sine: the sine ( sin) of an angle is equal to the length of the opposite (opp) side divided by the length of the hypotenuse (Hypot). sin θ = Opp / Hypot. Cosine: the cosine ( cos) of an angle is equal to the length of the ...This math video tutorial provides a basic introduction into trigonometry. It covers trigonometric ratios such as sine, cosine, and tangent. It explains how...The six basic trigonometric functions are: 1. Sine, #sintheta# 2. Cosine, #costheta# 3. Tangent, #tantheta# 4. Cotangent, #cottheta# 5. Secant, #sectheta# 6. Cosecant, #csctheta# Take the following triangle for example: Let the angle marked at A be #theta#. The longest side of the triangle is the hypotenuse, the side next to the angle is the …2. 51. a θ and ϕ are complements. b sinθ = cosϕ and cosθ = sinϕ. The side opposite θ is the side adjacent to ϕ, and vice versa. 53. a As θ increases, tanθ increases also. The side opposite θ increases in length while the side adjacent to θ remains fixed. b As θ increases, cosθ decreases. A debt-to-income ratio (DTI) is a tool lenders use to determine whether they believe you can manage additional debt. Read to find what's considered a good DTI. Get top content in o...Trigonometric functions include trigonometric ratios, compound angles and multiple angles, which are used to get consistent results. This article explains Trigonometric Ratios of Compound Angles along with solved examples. An angle is a ray rotated about the initial point. The point where the rotation starts is the initial side, and the point ...Similar Triangles and Trigonometric Ratios. A right triangle is a triangle with one of the angles being 90o . This is a special angle and the side opposite is called the hypotenuse. There are two other angles which are not distinguished but we may name them or assign a variable to represent their measure.Learn the basics of trigonometry, such as sine, cosine and tangent, and how to use them to find angles and distances in right-angled triangles. Explore the unit circle, degrees …0. ∞. The Trigonometric Ratios of standard angles are listed below 0°, 30°, 45°, 60° and 90°.The values of Trigonometric Ratios of standard angles are very helpful and important to solve the trigonometric problems. Therefore, it is necessary for you to remember the value of the Trigonometric Ratios of standard angles.Mar 4, 2023 · 1 Use measurements to calculate the trigonometric ratios for acute angles #1-10, 57-60. 2 Use trigonometric ratios to find unknown sides of right triangles #11-26. 3 Solve problems using trigonometric ratios #27-34, 41-46. 4 Use trig ratios to write equations relating the sides of a right triangle #35-40. Three Functions, but same idea. Right Triangle. Sine, Cosine and Tangent are the main functions used in Trigonometry and are based on a Right-Angled Triangle.. Before getting stuck into the functions, it helps to give a name to each side of a right triangle: The ratios sine, cosine, and tangent are the "regular" trig ratios; the cosecant, secant, and cotangent are their respective reciprocal ratios (that is, the values of the flipped-over fractions for the "regular" ratios). By the way, there is no requirement that Greek letters be used as the argument of (that is, the input to) a trig function.Nov 21, 2023 · The trigonometric ratios sin, cos and tan are defined as follows: Sine is the ratio between the Opposite side and the Hypothenuse, Cosine is the ratio between the Adjacent side and the Hypothenuse ... Practice these assortments of primary trigonometric ratio worksheets designed to benefit high school children with topics like finding trigonometric ratios using SOH-CAH-TOA; determine all the three primary trigonometric ratios of the right-angled triangle; find the value of sine, cosine and tangent; and more.For example, 120° and 30° are allied angles because their difference is 90°. Using the above points, we can say six trigonometric ratios sine, cosine, tangent, cotangent, cosecant, and secant. And when the two angles represent either 0°, 90°, or multiple of 90° in their addition or subtraction can be called allied angles.Feb 15, 2011 · Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/geometry-home/right-triangles-... 'Price is what you pay. Value is what you get.' -- Warren BuffettPutting his finger on this difference between price and value in stock investing is essentially what made ... © 202...The hypotenuse is NM. The hypotenuse is LN. The side adjacent ∠L is NM. The side adjacent ∠N is ML., Identify the triangle that contains an acute angle for which the sine and cosine ratios are equal., What are the values of the three trigonometric ratios for angle L, in simplest form? sin(L) = cos(L) = tan(L) = and more.The trigonometric ratios can be used to solve 3-dimensional close three-dimensional (3D) An object with width, height and depth, eg a cube. problems which involve calculating a length or an angle ...Lessons On Trigonometry Inverse trigonometry Trigonometry Worksheets. Special Angles: 30 and 60. Let us first consider 30˚ and 60˚. These two angles form a 30˚-60˚-90˚ right triangle as shown. The ratio of the sides of the triangle is 1:√3:2. From the triangle we get the ratios as follows: Special Angles: 45 and 90In trigonometry formulas, learn about all the basic formulas based on trigonometry ratios (sin, cos, tan) and identities as per Class 10, 11 and 12 syllabi. Also, find solved examples and practice problems of trigonometric formulas at GeeksforGeeks.31 Oct 2023 ... Trigonometric ratios formula for class 10 math students. Check out the complete series on TRIGONOMETRY using Animation and visual tools: ...Trigonometry (from Ancient Greek τρίγωνον (trígōnon) 'triangle', and μέτρον (métron) 'measure') [1] is a branch of mathematics concerned with relationships between angles and side lengths of triangles. In particular, the trigonometric functions relate the angles of a right triangle with ratios of its side lengths. The six basic trigonometric functions are: 1. Sine, #sintheta# 2. Cosine, #costheta# 3. Tangent, #tantheta# 4. Cotangent, #cottheta# 5. Secant, #sectheta# 6. Cosecant, #csctheta# Take the following triangle for example: Let the angle marked at A be #theta#. The longest side of the triangle is the hypotenuse, the side next to the angle is the …Trigonometry is the branch of math, but its ratios are widely used in architecture, physics, satellite navigation systems and many other calculations. With hands-on expertise in trigonometric ratios finding heights, studying waves, calculating distance and angles is an easy task.Step 2: Label the sides of the triangle according to the ratios of that special triangle. 30 ∘ 60 ∘ x 3 x 2 x. Step 3: Use the definition of the trigonometric ratios to find the value of the indicated expression. sin ( 30 ∘) = opposite hypotenuse = x 2 x = 1 x 2 x = 1 2. Note that you can think of x as 1 x so that it is clear that x 2 x ...How to use the trig ratios of special angles to find exact values of expressions involving sine, cosine and tangent values of 0, 30, 45, 60 and 90 degrees? Example: Determine the exact values of each of the following: a) sin30°tan45° + tan30°sin60°. b) cos30°sin45° + sin30°tan30°. Show Video Lesson.Dec 5, 2022 · Trigonometric Ratios. Trigonometry is all about triangles or to be more precise the relationship between the angles and sides of a right-angled triangle. There are three sides of a triangle named Hypotenuse, Adjacent, and Opposite. The ratio between these sides based on the angle between them is called Trigonometric Ratio. Learn the six trigonometric ratios of a right angle triangle and how to calculate them using formulas and mnemonics. See solved examples and a table of values for different …Trigonometric ratios are ratios of the sides of a right triangle given one of the non-right angles of the triangle. Recall that a right triangle always has one right angle with a measure of 90 degrees or π 2 radians. Therefore, knowing one of the other angles means the third angle is also known. Since all triangles have 180 degrees or π ... 8.2: The Trigonometric Ratios. There are six common trigonometric ratios that relate the sides of a right triangle to the angles within the triangle. The three standard ratios are the sine, cosine and tangent. These are often abbreviated sin, cos and tan. Looking at our trig cheatsheet, we find an easy ratio where we can compare secant to 1. For example, secant to 1 (hypotenuse to horizontal) is the same as 1 to cosine: Suppose our secant is 3.5, i.e. 350% of the radius of the unit circle. What’s the angle to the wall? Appendix: A Few Examples. Example: Find the sine of angle x.Practice these assortments of primary trigonometric ratio worksheets designed to benefit high school children with topics like finding trigonometric ratios using SOH-CAH-TOA; determine all the three primary trigonometric ratios of the right-angled triangle; find the value of sine, cosine and tangent; and more.Compa ratio is a formula used to assess the competitiveness of an employee’s pay. Learn how to calculate compa ratio. Human Resources | What is WRITTEN BY: Charlette Beasley Publis...Any fast way of remebering trigonometric ratios of compound angles. 0. Alternative of finding theta when sin $\theta$ and cos $\theta$ are given. 0. Understanding this solution for a trigonometric identity of $\tan2 \theta$ 5. Solving $2\cos\left(2\theta\right) = \sqrt{3}$ 0.Discover how to measure angles, distances, and heights using trigonometric ratios and the unit circle. Learn how to use sine, cosine, and tangent to solve real-world problems involving triangles and circular motion. Right Triangle Trigonometry Trigonometric Ratios Example Find the sine, cosine, and tangent ratios for each of the acute angles in the following triangle. Solution: We first find the missing length of side RS. Solving the equation ( ) 12 13RS 22 2+=, we obtain RS =5. We then find the three basic trigonometric ratios for angle R:A microalbumin creatinine ratio test measures the amount of albumin in urine. Albumin in urine may be a sign of kidney disease. Learn more. Microalbumin creatinine ratio urine test...Debt-to-Income Ratio Calculator I believe it does if you have a ton of arrears I do believe they can collect. And attach to your credit report. At least that's what's wrong with mi...Once you know the value of sine and cosine, you can use the following trigonometric identities to obtain the values of the other four functions: Tangent is the sine-to-cosine ratio. tan(α) = sin(α)/cos(α) Cosecant is the reciprocal of the sine. csc(α) = 1/sin(α) Secant is the reciprocal of the cosine. sec(α) = 1/cos(α)Apr 26, 2021 · There are six trigonometric ratios in total: sine, cosine, tangent, and their reciprocals, cosecant, secant and cotangent. Trigonometric functions are real functions which relate an angle of a right triangle to ratios of two side lengths, with a defined range and domain. Each of these six trigonometric functions has a corresponding inverse ... Trigonometric ratios in right triangles. Google Classroom. β 4 5 3 C B A. Find tan ( β) in the triangle. Trigonometry Ratios-Sine, Cosine, Tangent. The trigonometric ratios of a triangle are also called the trigonometric functions. Sine, cosine, and tangent are 3 important trigonometric functions and are abbreviated as sin, cos and tan. Let us see how are these ratios or functions, evaluated in case of a right-angled triangle.Practice these assortments of primary trigonometric ratio worksheets designed to benefit high school children with topics like finding trigonometric ratios using SOH-CAH-TOA; determine all the three primary trigonometric ratios of the right-angled triangle; find the value of sine, cosine and tangent; and more.This page titled 11.1: The Trigonometric Ratios is shared under a GNU Free Documentation License 1.3 license and was authored, remixed, and/or curated by …Trigonometry values of different ratios, such as sine, cosine, tangent, secant, cotangent, and cosecant, deal with the measurement of lengths and angles of the right-angle triangle. The values of trigonometric functions for 0°, 30°, 45°, 60° and 90° are commonly used to solve trigonometry problems.. Trigonometry values are all about the study of standard …In this section we learn about the trigonometric ratios as well as SOH CAH TOA, which is an acronym for memorizing the ratios. Each of the three trigonometric ratios is listed below. In each case we state the formula as well as illustrate it with two examples (one for each of the interior angles, $a$ and $b$, of the triangle). We can use this right triangle to redefine sine, cosine, and the other trigonometric functions as ratios of the sides of a right triangle. Figure 1. We know. cos t = x 1 = x cos t = x 1 = x. Likewise, we know. sin t = y 1 = y sin t = y 1 = y.When it comes to working with mortar, achieving the perfect mix ratio is crucial. The mix ratio determines the strength and durability of the mortar, ensuring that it can withstand...William Sharpe's Sharpe ratio is a measure of risk-adjusted returns used to determine the best or worst returns given volatility within a market. The Sharpe ratio measures the abil...Basis of trigonometry: if two right triangles have equal acute angles, they are similar, so their corresponding side lengths are proportional.. In mathematics, the trigonometric functions (also called circular functions, angle functions or goniometric functions) are real functions which relate an angle of a right-angled triangle to ratios of two side lengths. In a right triangle, the hypotenuse is the longest side, an "opposite" side is the one across from a given angle, and an "adjacent" side is next to a given angle. We use special words to describe the sides of right triangles. The hypotenuse of a right triangle is always the side opposite the right angle. It is the longest side in a right triangle.Trigonometry Unit 1: Right Triangles and the Pythagorean Theorem 1.8: Special Right Triangles and Ratios Expand/collapse global location ... Note that the order of the side ratios $x,x\sqrt{3},2x$ and $x, x, x\sqrt{2}$ is important because each side ratio has a corresponding angle. In all triangles, the smallest sides correspond to smallest ...The important angles in trigonometry are 0°, 30°, 45°, 60°, 90°, 180°, 270° and 360°. And the important six trigonometric ratios or functions are sine, cosine, tangent, cosecant, secant and cotangent. Before discussing the trig angles, let us have a look at the definition of angle, and its related terminologies.Accurate trigonometric ratios for 0°, 30°, 45°, 60° and 90° The trigonometric ratios for the angles 30°, 45° and 60° can be calculated using two special triangles. Learn what trigonometric ratios are and how to calculate them using the sides of a right triangle. Find the values of trigonometric ratios for standard angles and identities for different types of angles.Key Terms. Trigonometric Ratios: ratios that relate the lengths of the sides of right triangles to their interior angles. Sine: the sine ( sin) of an angle is equal to the length of the opposite (opp) side divided by the length of the hypotenuse (Hypot). sin θ = Opp / Hypot. Cosine: the cosine ( cos) of an angle is equal to the length of the ...Trigonometric ratios are Sine, Cosine, Tangent, Cotangent, Secant and Cosecant. The standard angles for these trigonometric ratios are 0 °, 30°, 45°, 60° and 90°. These angles can also be represented in the form of radians such as 0, π/6, π/4, π/3, and π/2. These angles are most commonly and frequently used in trigonometry.Trigonometry is a branch of mathematics that explores the relationships between the ratios of the sides of a right-angled triangle and its angles.. The fundamental ratios used to study these relationships are known as trigonometric ratios, which include sine, cosine, tangent, cotangent, secant, and cosecant.25 Jun 2012 ... This video is part of an online course, Intro to Physics. Check out the course here: https://www.udacity.com/course/ph001.Learn how to use the trip ratios to find missing side lengths. Do you remember SOHCHATOA ? This is an easy way to remember the trigonometric ratios. Sine eq...Lessons On Trigonometry Inverse trigonometry Trigonometry Worksheets. Special Angles: 30 and 60. Let us first consider 30˚ and 60˚. These two angles form a 30˚-60˚-90˚ right triangle as shown. The ratio of the sides of the triangle is 1:√3:2. From the triangle we get the ratios as follows: Special Angles: 45 and 90Trigonometry is a branch of mathematics that explores the relationships between the ratios of the sides of a right-angled triangle and its angles.. The fundamental ratios used to study these relationships are known as trigonometric ratios, which include sine, cosine, tangent, cotangent, secant, and cosecant.The hypotenuse is NM. The hypotenuse is LN. The side adjacent ∠L is NM. The side adjacent ∠N is ML., Identify the triangle that contains an acute angle for which the sine and cosine ratios are equal., What are the values of the three trigonometric ratios for angle L, in simplest form? sin(L) = cos(L) = tan(L) = and more.Based on this definition, people have found the THEORETICAL value of trigonometric ratios for obtuse, straight, and reflex angles. This value of the trigonometric ratios for these angles no longer represent a ratio, but rather a value that fits a pattern for the actual ratios. I hope this helped! Proof of [cos(θ)]^2+[sin(θ)]^2=1:The trig ratios can be used to find lots of information, and one of their main purposes is to help solve triangles. To solve a triangle means to find the length of all the sides and the measure of all the angles. This lesson will cover how to use trig ratios to find the side lengths of a triangle. There are three steps: 1.Six trigonometric ratios for right angle triangle are Sine(sin), Cosecant(Cos), Tangent(Tan), Cosecant(Cos), Secant(Sec), Cotangent(Cot) respectively. We will learn the sin, cos, tan formulas for these trigonometric ratios and easy ways to memorize it.. Trigonometry definition: Branch of Mathematics which deals with the measurement of …Trigonometric ratios are the ratios of the side lengths of a right-angled triangle. Three common trigonometric ratios are the sine (sin), cosine (cos), and tangent (tan). There are three more trigonometric …3 Aug 2023 ... The three primary trigonometric ratios are sine (sin), cosine (cos), and tangent (tan). ... To find these ratios, you need to follow these steps:.Hummingbirds are fascinating creatures that bring joy and beauty to any garden. To attract these delightful birds, many people set up hummingbird feeders filled with sugar water. M...There are basic 6 trigonometric ratios used in trigonometry, also called trigonometric functions- sine, cosine, secant, co-secant, tangent, and co-tangent, written as sin, cos, sec, csc, tan, cot in short. The …Learn how to calculate and use the trigonometric ratios of sine, cosine and tangent based on a right triangle. See examples, graphs, animations and exercises to practice …Learn about trigonometry, the branch of mathematics that deals with angles and their functions. Explore the history, applications, and formulas of trigonometric ratios and identities in plane and spherical …Jul 24, 2017 · This math video tutorial provides a basic introduction into trigonometry. It covers trigonometric ratios such as sine, cosine, and tangent. It explains how... Learn the definition, formula, and examples of sin, cos, and tan, the trigonometric ratios that relate the angles and sides of right triangles. Watch a video tutorial and see how to use SOH CAH TOA to solve for any angle or side. Trigonometric Ratios: Cosine. Right triangles have ratios that are used to represent their base angles. Cosine ratios, along with sine and tangent ratios, are ratios of two different sides of a right triangle.Cosine ratios are specifically the ratio of the side adjacent to the represented base angle over the hypotenuse.There are basic 6 trigonometric ratios used in trigonometry, also called trigonometric functions- sine, cosine, secant, co-secant, tangent, and co-tangent, written as sin, cos, sec, csc, tan, cot in short. The …The tangent ratios refer to the side's ratios opposite to the length adjacent to the angle they represent. The other trigonometric ratios, cosecant, secant and cotangent are reciprocals to the basic trigonometric ratios: sine, cosine and tangent. The secant ratio describes the hypotenuse ratio to any side opposite to a given angle of a right ...To determine the trigonometric ratios of angles 240° and 225°, we find the trigonometric ratios of the equivalent angles measured in the counterclockwise direction from negative x axis (180° axis), that is, 240° – 180° = 60° and 225° – 180° = 45° respectively, while taking into account the positive or negative distance of a point ...Meetings where decisions are made but no one wants to be accountable for them, are the worst meetings. Keep that “action to decision” ratio low by ending every meeting with an “acc...Trigonometric ratios show how long one side of the triangle is compared to another. The 3 important ratios are known as the sine (sin), cosine (cos) and tangent (tan) of the angle:Hummingbirds are fascinating creatures that bring joy and beauty to any garden. To attract these delightful birds, many people set up hummingbird feeders filled with sugar water. M...Trigonometric Ratios of Complementary Angles Examples. To have a better insight on trigonometric ratios of complementary angles consider the following example. Example: If A, B and C are the interior angles of a right-angle triangle, right-angled at B then find the value of A, given that tan 2A = cot(A – 30°) and 2A is an acute angle. ...Introduction to the trigonometric ratios. Solving for a side in a right triangle using the trigonometric ratios. Solving for an angle in a right triangle using the trigonometric ratios. Modeling with right triangles. See 3 more. Start quiz. The law of sines. Learn.Compa ratio is a formula used to assess the competitiveness of an employee’s pay. Learn how to calculate compa ratio. Human Resources | What is WRITTEN BY: Charlette Beasley Publis...

To do so: -Enter 0.30 on your calculator. -Find the Inverse button, then the Cosine button (This could also be the Second Function button, or the Arccosine button). Should come out to 72.542397, rounded. To round to the nearest hundredth of a degree, we round to 2 decimal, places, giving the answer 72.54. 2 comments.. Last of us game reviews

A microalbumin creatinine ratio test measures the amount of albumin in urine. Albumin in urine may be a sign of kidney disease. Learn more. Microalbumin creatinine ratio urine test...Trigonometric ratios in right triangles. Google Classroom. β 4 5 3 C B A. Find tan ( β) in the triangle. Activity 2.1 Trigonometric Ratios. Two related quantities or variables are proportional if their ratio is always the same. 1 a On any given day, the cost of filling up your car’s gas tank is proportional to the number of gallons of gas you buy. For each purchase below, compute the ratio. Activity 2.1 Trigonometric Ratios. Two related quantities or variables are proportional if their ratio is always the same. 1 a On any given day, the cost of filling up your car’s gas tank is proportional to the number of gallons of gas you …1.2: The Trigonometric Ratios. There are six common trigonometric ratios that relate the sides of a right triangle to the angles within the triangle. The three standard ratios are the sine, cosine and tangent. These are often abbreviated sin, cos and tan. Discover how to measure angles, distances, and heights using trigonometric ratios and the unit circle. Learn how to use sine, cosine, and tangent to solve real-world problems involving triangles and circular motion.Apr 26, 2021 · There are six trigonometric ratios in total: sine, cosine, tangent, and their reciprocals, cosecant, secant and cotangent. Trigonometric functions are real functions which relate an angle of a right triangle to ratios of two side lengths, with a defined range and domain. Each of these six trigonometric functions has a corresponding inverse ... Special angles are angles that have values that are common in trigonometry exercises and in everyday life in general. Generally, the special angles are considered to be the angles of 30°, 45°, and 60°. These angles have trigonometric ratios that are easy to remember. Here, we will learn about the trigonometric ratios of the special angles 30 ...While a company's stock price reflects the value that investors are placing on that investment, the price-to-earnings ratio, called P/E ratio, illustrates a stock's worth based on ...Looking at our trig cheatsheet, we find an easy ratio where we can compare secant to 1. For example, secant to 1 (hypotenuse to horizontal) is the same as 1 to cosine: Suppose our secant is 3.5, i.e. 350% of the radius of the unit circle. What’s the angle to the wall? Appendix: A Few Examples. Example: Find the sine of angle x.'Price is what you pay. Value is what you get.' -- Warren BuffettPutting his finger on this difference between price and value in stock investing is essentially what made ... © 202...21 Dec 2018 ... This tutorial discusses the three primary trigonometric ratios (sin, cos & tan). The video shows how to label sides as hypotenuse, ...Determine the six trigonometric ratios for angle A in the right triangle below. So this right over here is angle A, it's at vertex A. And to help me remember the definitions of the trig ratios-- and these are human constructed definitions that have ended up being very, very useful for analyzing a whole series of things in the world.Right Triangle Trigonometry Trigonometric Ratios Example Find the sine, cosine, and tangent ratios for each of the acute angles in the following triangle. Solution: We first find the missing length of side RS. Solving the equation ( ) 12 13RS 22 2+=, we obtain RS =5. We then find the three basic trigonometric ratios for angle R:The trigonometric ratios only work for the non-right angles, in this case either angle 𝐴 or angle 𝐵. We know that the measure of angle 𝐵 is 50°, so let's use that. – – – In a triangle, the side opposite of an angle is the side that does not help form the angle. Get your free lessons: https://vividmath.comHow to find Trigonometric Ratios in a Right Angled Triangle (SOHCAHTOA).See all Trigonometry lessons: https://viv...Looking at our trig cheatsheet, we find an easy ratio where we can compare secant to 1. For example, secant to 1 (hypotenuse to horizontal) is the same as 1 to cosine: Suppose our secant is 3.5, i.e. 350% of the radius of the unit circle. What’s the angle to the wall? Appendix: A Few Examples. Example: Find the sine of angle x.Trigonometry (from Ancient Greek τρίγωνον (trígōnon) 'triangle', and μέτρον (métron) 'measure') [1] is a branch of mathematics concerned with relationships between angles and side lengths of triangles. In particular, the trigonometric functions relate the angles of a right triangle with ratios of its side lengths. Jan 18, 2024 · Using area and one side for right triangle trig calculation. If you know a a or b b, use the right triangle area formula that relates the base ( b b) to the height ( a a) and solve for the unknown side: Given a: b = 2 × Area / a. b = 2 \times \text {Area}/a b = 2× Area/a; and. Given b: 2. 51. a θ and ϕ are complements. b sinθ = cosϕ and cosθ = sinϕ. The side opposite θ is the side adjacent to ϕ, and vice versa. 53. a As θ increases, tanθ increases also. The side opposite θ increases in length while the side adjacent to θ remains fixed. b As θ increases, cosθ decreases. The gold-silver ratio is measure of how many ounces of silver it takes to buy an ounce of gold. The gold-silver ratio is measure of how many ounces of silver it takes to buy an oun....

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