91Ó°ÊÓ

In Exercises 1-18, solve each of the trigonometric equations exactly over the indicated intervals. $$ \cos \theta=-\frac{\sqrt{2}}{2}, 0 \leq \theta<2 \pi $$

In Exercises \(25-36\), use a calculator to evaluate each expression. Give the answer in degrees and round to two decimal places. $$ \tan ^{-1}(1.895) $$

In Exercises \(25-36\), use a calculator to evaluate each expression. Give the answer in degrees and round to two decimal places. $$ \tan ^{-1}(3.2678) $$

In Exercises 1-36, solve each of the trigonometric equations exactly on the interval \(0 \leq x<2 \pi\). $$ \cos (3 x) \cos (2 x)+\sin (3 x) \sin (2 x)=1 $$

In Exercises \(25-36\), use a calculator to evaluate each expression. Give the answer in degrees and round to two decimal places. $$ \csc ^{-1}(-6.1324) $$

In Exercises 19-36, solve each of the trigonometric equations exactly on \(0 \leq \theta<2 \pi\). $$ 2 \sec ^{2} \theta+\sec \theta=1 $$

In Exercises 37-48, solve each of the trigonometric equations on the interval \(0^{\circ} \leq \theta<360^{\circ}\). Give answers in degrees and round to two decimal places. $$ 6 \cos ^{2} x+\sin x=5 $$

Use the graphs of \(y=\tan x\) and \(y=\cos x+1\) to determine the number of solutions to the equation \(\tan x=\cos x+1\) on the interval \([0,2 \pi)\).

Solve for the smallest positive \(x\) that makes this statement true: $$ \cos x \cos 15^{\circ}+\sin x \sin 15^{\circ}=0.7 $$

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 \(\left[\frac{\pi}{6}, \frac{5 \pi}{6}\right]\).