College Algebra & Trigonometry, 2018a

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8.2. THE TRIGONOMETRIC RATIOS 351 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. The other three (cosecant, secant and cotangent) are the reciprocals of the sine, cosine and tangent and are often abbreviated csc, sec, and cot. θ hypotenuse adjacent opposite Given an angle situated in a right triangle, the sine function is defined as the ratio of the side opposite the angle to the hypotenuse, the cosine is defined as the ratio of the side adjacent to the angle to the hypotenuse and the tangent is defined as the ratio of the side opposite the angle to the side adjacent to the angle. sin θ = opp hyp cos θ = adj hyp tan θ = opp adj A common mneumonic device to help remember these relationships is –SOHCAHTOA– which identifies the Sin as Opp over Hyp Cos as Adj over Hyp and the Tan as Opp over Adj.
352 CHAPTER 8. RIGHT TRIANGLE TRIGONOMETRY An acute angle placed in the other position of a right triangle would have different oppposite and adjacent sides although the hypotenuse would remain the same. hypotenuse opposite α adjacent Examples: Trigonometric Ratios Find sin θ, cos θ and tan θ for the given angle θ 3 θ 5 In order to find the sin and cos of the angle θ, we must first find the hypotenuse by using the Pythagorean Theorem (a 2 + b 2 = c 2 ).
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College Algebra & Trigonometry
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c○2018 Richard W. Beveridge This
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4 CONTENTS 2.4 Solution of Rational
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6 CONTENTS 8.2 The Trigonometric Ra
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8 CONTENTS
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10 CHAPTER 1. ALGEBRA REVIEW Exampl
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88 CHAPTER 2. POLYNOMIAL AND RATION
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100 CHAPTER 2. POLYNOMIAL AND RATIO
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190 CHAPTER 4. FUNCTIONS by substit
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192 CHAPTER 4. FUNCTIONS 4.2 Domain
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194 CHAPTER 4. FUNCTIONS Exercises
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196 CHAPTER 4. FUNCTIONS 8) 12 10 8
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198 CHAPTER 4. FUNCTIONS We can use
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200 CHAPTER 4. FUNCTIONS 3) 20 16 1
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202 CHAPTER 4. FUNCTIONS Vertical S
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258 CHAPTER 5. CONIC SECTIONS - CIR
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288 CHAPTER 6. SEQUENCES AND SERIES
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College Algebra & Trigonometry, 2018a

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