College Algebra & Trigonometry, 2018a

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10.3. TRIGONOMETRIC EQUATIONS 465 Exercises 10.3 Find all solutions for 0 ◦ ≤ x
466 CHAPTER 10. TRIGONOMETRIC IDENTITIES AND EQUATIONS 10.4 More Trigonometric Equations When the solution to a trigonometric equation is one of the quadrantal angles (0 ◦ ,90 ◦ , 180 ◦ , 270 ◦ and so on), then determining all the solutions between 0 ◦ and 360 ◦ can work a little differently. The calculator will return some of these values, but in some cases it may not. If we go back to the unit circle, we can see this more clearly: (cos 90 ◦ , sin 90 ◦ ) (0, 1) (cos 180 ◦ , sin 180 ◦ ) (−1, 0) (cos 0 ◦ , sin 0 ◦ ) (1, 0) (0, −1) (cos 270 ◦ , sin 270 ◦ ) In the diagram above we can see the sine and cosine for 0 ◦ ,90 ◦ , 180 ◦ , and 270 ◦ . Since tan θ = sin θ cos θ , then we can see that tan 0◦ =0, tan 90 ◦ is undefined, tan 180 ◦ = 0 and tan 270 ◦ is also undefined. The real issue with the quadrantal angles is finding sin −1 (0), cos −1 (0) or tan −1 (0). The calculator returns values of: sin −1 (0) = 0 ◦ cos −1 (0) = 90 ◦ tan −1 (0) = 0 ◦ In each case, there is another possibility than differs from the given angle by 180 ◦ , so:
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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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12 CHAPTER 1. ALGEBRA REVIEW 2(x +3
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16 CHAPTER 1. ALGEBRA REVIEW Trinom
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20 CHAPTER 1. ALGEBRA REVIEW (3x ?)
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30 CHAPTER 1. ALGEBRA REVIEW Then,
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40 CHAPTER 1. ALGEBRA REVIEW devise
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42 CHAPTER 1. ALGEBRA REVIEW −7i(
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44 CHAPTER 1. ALGEBRA REVIEW Exerci
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46 CHAPTER 1. ALGEBRA REVIEW 43) (3
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88 CHAPTER 2. POLYNOMIAL AND RATION
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100 CHAPTER 2. POLYNOMIAL AND RATIO
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140 CHAPTER 3. EXPONENTS AND LOGARI
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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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204 CHAPTER 4. FUNCTIONS Now, if, i
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206 CHAPTER 4. FUNCTIONS So the gra
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208 CHAPTER 4. FUNCTIONS Stretching
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210 CHAPTER 4. FUNCTIONS Multiplyin
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214 CHAPTER 4. FUNCTIONS 3) Match e
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216 CHAPTER 4. FUNCTIONS 6) f(x) 7)
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218 CHAPTER 4. FUNCTIONS Being fami
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222 CHAPTER 4. FUNCTIONS 4.6 Piecew
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238 CHAPTER 4. FUNCTIONS 2) The gra
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242 CHAPTER 4. FUNCTIONS 8) A recta
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250 CHAPTER 4. FUNCTIONS The graph
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256 CHAPTER 4. FUNCTIONS 3) A power
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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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