91Ó°ÊÓ

If \(\alpha, \beta,\) and \(\gamma\) are angles in the same triangle, then prove or disprove \(\sin (\alpha+\beta)=\sin \gamma\)

Explain how to determine the reduction identities from the double-angle identity \(\cos (2 x)=\cos ^{2} x-\sin ^{2} x\)

Explain how to determine the double-angle formula for \(\tan (2 x)\) using the double-angle formulas for \(\cos (2 x)\) and \(\sin (2 x)\)

For the following exercises, find the exact values of a \() \sin (2 x),\) b) \(\cos (2 x),\) and \(c ) \tan (2 x)\) without solving for \(x\) If \(\sin x=\frac{1}{8}, \quad\) and \(x\) is in quadrant I.

For the following exercises, find the exact values of a \() \sin (2 x),\) b) \(\cos (2 x),\) and \(c ) \tan (2 x)\) without solving for \(x\) If \(\cos x=\frac{2}{3}, \quad\) and \(x\) is in quadrant I.

For the following exercises, find the exact values of a \() \sin (2 x),\) b) \(\cos (2 x),\) and \(c ) \tan (2 x)\) without solving for \(x\) If \(\cos x=-\frac{1}{2},\) and \(x\) is in quadrant III.

For the following exercises, find the exact values of a \() \sin (2 x),\) b) \(\cos (2 x),\) and \(c ) \tan (2 x)\) without solving for \(x\) If \(\tan x=-8,\) and \(x\) is in quadrant IV.

For the following exercises, find the values of the six trigonometric functions if the conditions provided hold. $$ \cos (2 \theta)=\frac{3}{5} \text { and } 90^{\circ} \leq \theta \leq 180^{\circ} $$

For the following exercises, find the values of the six trigonometric functions if the conditions provided hold. $$ \cos (2 \theta)=\frac{1}{\sqrt{2}} \text { and } 180^{\circ} \leq \theta \leq 270^{\circ} $$

For the following exercises, simplify to one trigonometric expression. $$ 2 \sin \left(\frac{\pi}{4}\right) 2 \cos \left(\frac{\pi}{4}\right) $$