91Ó°ÊÓ

For the following exercises, find exact solutions on the interval \([0,2 \pi) .\) Look for opportunities to use trigonometric identities. $$ \tan x=3 \sin x $$

For the following exercises, find exact solutions on the interval \([0,2 \pi) .\) Look for opportunities to use trigonometric identities. $$ \cos ^{3} t=\cos t $$

For the following exercises, algebraically determine all solutions of the trigonometric equation exactly, then verify the results by graphing the equation and finding the zeros. $$ 6 \sin ^{2} x-5 \sin x+1=0 $$

For the following exercises, algebraically determine all solutions of the trigonometric equation exactly, then verify the results by graphing the equation and finding the zeros. $$ 8 \cos ^{2} x-2 \cos x-1=0 $$

For the following exercises, algebraically determine all solutions of the trigonometric equation exactly, then verify the results by graphing the equation and finding the zeros. $$ 100 \tan ^{2} x+20 \tan x-3=0 $$

For the following exercises, algebraically determine all solutions of the trigonometric equation exactly, then verify the results by graphing the equation and finding the zeros. $$ 20 \sin ^{2} x-27 \sin x+7=0 $$

For the following exercises, algebraically determine all solutions of the trigonometric equation exactly, then verify the results by graphing the equation and finding the zeros. $$ 2 \tan ^{2} x+7 \tan x+6=0 $$

For the following exercises, algebraically determine all solutions of the trigonometric equation exactly, then verify the results by graphing the equation and finding the zeros. $$ 130 \tan ^{2} x+69 \tan x-130=0 $$

For the following exercises, use a calculator to find all solutions to four decimal places. $$ \sin x=0.27 $$

For the following exercises, use a calculator to find all solutions to four decimal places. $$ \sin x=-0.55 $$