91Ó°ÊÓ

Find all real numbers that satisfy each equation. Round approximate answers to 2 decimal places. $$ \frac{\sin 33.2^{\circ}}{a}=\frac{\sin 45.6^{\circ}}{13.7} $$

Find the exact value of each composition without using a calculator or table. $$ \sin \left(\csc ^{-1}(-2)\right) $$

Find all real numbers in the interval \([0,2 \pi]\) that satisfy each equation. $$ \tan (x)-\tan (2 x)=1+\tan (x) \tan (2 x) $$

Find all real numbers that satisfy each equation. Round approximate answers to 2 decimal places. $$ \frac{\sin 49.6^{\circ}}{55.1}=\frac{\sin 88.2^{\circ}}{b} $$

Find all values of \(\theta\) in the interval of \(\left[0^{\circ}, 360^{\circ}\right)\) that satisfy each equation. Round approximate answers to the nearest tenth of a degree. $$ 4 \sin ^{4} \theta-5 \sin ^{2} \theta+1=0 $$

One way to solve an equation with a graphing calculator is to rewrite the equation with 0 on the right-hand side, then graph the function that is on the left-hand side. The \(x\) -coordinate of each \(x\) -intercept of the graph is a solution to the original equation. For each equation find all real solutions (to the nearest tenth) in the interval \([0,2 \pi)\). $$ \sin (x / 2)=\cos (3 x) $$

Find the exact value of each composition without using a calculator or table. $$ \sin ^{-1}(\sin (3 \pi / 4)) $$

Find all real numbers that satisfy each equation. Round approximate answers to 2 decimal places. $$ \frac{\sin x}{8.5}=\frac{\sin (\pi / 7)}{6.3} $$

One way to solve an equation with a graphing calculator is to rewrite the equation with 0 on the right-hand side, then graph the function that is on the left-hand side. The \(x\) -coordinate of each \(x\) -intercept of the graph is a solution to the original equation. For each equation find all real solutions (to the nearest tenth) in the interval \([0,2 \pi)\). $$ 2 \sin (x)=\csc (x+0.2) $$

Find all values of \(\theta\) in the interval of \(\left[0^{\circ}, 360^{\circ}\right)\) that satisfy each equation. Round approximate answers to the nearest tenth of a degree. $$ \cot ^{4} \theta-4 \cot ^{2} \theta+3=0 $$