91Ó°ÊÓ

In Exercises 75-78, find the smallest positive value of \(x\) that makes the statement true. Give the answer in degrees and round to two decimal places. $$ e^{x}-\tan x=0 $$

In Exercises 75-78, determine whether each statement is true or false. The solution set for the equation \(\sin ^{2} x=0.5 \sin x\) for \(0 \leq x<2 \pi\) is \(\left[\frac{\pi}{6}, \frac{5 \pi}{6}\right]\).

In Exercises 69-88, evaluate each expression exactly. $$ \csc \left[\sin ^{-1}\left(\frac{1}{4}\right)\right] $$

In Exercises 69-88, evaluate each expression exactly. $$ \cot \left[\sin ^{-1}\left(\frac{60}{61}\right)\right] $$

How many solutions does the equation \(\sin \left(k x+\frac{\pi}{2}\right)=1\) have on the interval \([0,2 \pi)\) for integer \(k\) ?

In Exercises 69-88, evaluate each expression exactly. $$ \cot \left[\sec ^{-1}\left(\frac{41}{9}\right)\right] $$

$$ \text { Solve } 16 \sin ^{4} \theta-8 \sin ^{2} \theta=-1 \text { over } 0 \leq \theta \leq 2 \pi \text {. } $$

In Exercises 69-88, evaluate each expression exactly. $$ \cos \left[\tan ^{-1}\left(\frac{3}{4}\right)-\sin ^{-1}\left(\frac{4}{5}\right)\right] $$

$$ \text { Solve }\left|\cos \left(\theta+\frac{\pi}{4}\right)\right|=\frac{\sqrt{3}}{2} \text { over all real numbers. } $$

In Exercises 69-88, evaluate each expression exactly. $$ \cos \left[\tan ^{-1}\left(\frac{12}{5}\right)+\sin ^{-1}\left(\frac{3}{5}\right)\right] $$