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CHAPTER 20 REVIEW EXERCISES

CONCEPT CHECK EXERCISES

Determine each of the following as being either true or false. If it is false, explain why.

$\tan 2 θ = \frac{\cos 2 θ}{\sin 2 θ}$
$\cos^{2} 2 α = 1 - \sin^{2} 2 α$
$\cos (α - β) = \cos α \cos β - \sin α \sin β$
$\sin \frac{α}{2} = \sqrt{\frac{1 - \cos α}{2}}$
$\sin^{- 1} (- 1) = \frac{3 π}{2}$
For $0 \leq θ < 2 π,$ the solution of the equation $2 \cos θ + 1 = 0$ is $θ = 2 π / 3, 4 π / 3$ .

PRACTICE AND APPLICATIONS

In Exercises 7–14, determine the values of the indicated functions in the given manner.

Find $\sin 120 °$ by using $120 ° = 90 ° + 30 ° .$
Find $\cos 30 °$ by using $30 ° = 90 ° - 60 ° .$
Find $\sin 315 °$ by using $315 ° = 360 ° - 45 ° .$
Find $\tan \frac{5 π}{4}$ by using $\frac{5 π}{4} = π + \frac{π}{4} .$
Find $\cos π$ by using $π = 2 (\frac{π}{2}) .$
Find $\sin \frac{3 π}{2}$ by using $\frac{3 π}{2} = 2 (\frac{3 π}{4}) .$
Find $\tan 60 °$ by using ...

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