College Algebra & Trigonometry, 2018a

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8.2. THE TRIGONOMETRIC RATIOS 355 Using the Pythagorean Theorem, we can find the missing side of the triangle: a 2 +1 2 =3 2 a 2 +1=9 a 2 =8 a = √ 8=2 √ 2 √ √ Then sin θ = 8 3 and tan θ = 8 1 = √ 8. You might say to yourself, “Wait a minute, just because the cosine of the angle θ is 1 3 , that doesn’t necessarily mean that the sides of the triangle are 1 and 3, they could be 2 and 6, or 3 and 9 or any values n and 3n.” This is true, and if the sides are expressed as n and 3n, then the missing side would be n √ 8, so that whenever we find a trigonometric ratio, the n’s will cancel out, so we just leave them out to begin with and call the sides 1 and 3. Example √ Given that tan θ = 5 7 , find sin θ and cos θ. First we’ll take the infomation about the tangent and use this to draw a triangle. √ 5 7 θ
356 CHAPTER 8. RIGHT TRIANGLE TRIGONOMETRY Then use the Pythagorean Theorem to find the missing side of the triangle: √ 5 2 +7 2 = c 2 5+49=c 2 54 = c 2 √ 54 = 3 √ 6=c So then: √ sin θ = √ 5 = 54 √ 5 54 cos θ = 7 √ 54 = 7 3 √ 6
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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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198 CHAPTER 4. FUNCTIONS We can use
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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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