91Ó°ÊÓ

Use identities to find each exact value. (Do not use a calculator.). $$\cos \left(-15^{\circ}\right)$$

Write short answers. Consider the inverse tangent function, defined by \(y=\tan ^{-1} x,\) or \(y=\arctan x\) (a) What is its domain? (b) What is its range? (c) Is this function increasing or decreasing? (d) Is there any real number \(x\) for which arctan \(x\) is not defined? If so, what is it (or what are they)?

Find \(\sin \theta\) $$\cot \theta=-\frac{1}{5}, \theta \text { in quadrant IV }$$

Use identities to find values of the sine and cosine functions for each angle measure. $$2 x, \text { given } \tan x=2 \text { and } \cos x > 0$$

Find \(\sin \theta\) $$\cot \theta=-\frac{1}{3}, \theta \text { in quadrant IV }$$

Lindsay solved the equation \(\sin x=1-\cos x\) by squaring each side to get $$ \sin ^{2} x=1-2 \cos x+\cos ^{2} x $$ Several steps later, using correct algebra, she concluded that the solution set for solutions over the interval \([0,2 \pi)\) is \(\left\\{0, \frac{\pi}{2}, \frac{3 \pi}{2}\right\\} .\) Explain why this is not the correct solution set.

Perform each indicated operation and simplify the result so that there are no quotients. $$(1+\tan \theta)^{2}-2 \tan \theta$$

Use identities to find each exact value. (Do not use a calculator.). $$\cos 105^{\circ}$$

Use identities to find values of the sine and cosine functions for each angle measure. $$2 \theta, \text { given } \sin \theta=-\frac{\sqrt{5}}{7} \text { and } \cos \theta > 0$$

Find \(\sin \theta\) $$\cos (-\theta)=\frac{\sqrt{5}}{5}, \tan \theta<0$$