91Ó°ÊÓ

Use a double-angle or half-angle identity to verify the given identity. $$\sin ^{2} x+\cos 2 x=\cos ^{2} x$$

Solve each equation, where \(0^{\circ} \leq x<360^{\circ} .\) Round approximate solutions to the nearest tenth of a degree. $$\frac{2}{5} \cos x-\frac{1}{2}=\frac{1}{3}-\frac{1}{2} \cos x$$

Find the exact value of the given expression. If an exact value cannot be given, give the value to the nearest ten-thousandth. $$\cos ^{-1}\left(\cos \frac{5 \pi}{4}\right)$$

Perform the indicated operations where \(u=3 i-2 j\) and \(v=-2 i+3 j\). $$\|\mathbf{v}\|$$

Use a double-angle or half-angle identity to verify the given identity. $$\sin ^{2} x+\cos 2 x=\cos ^{2} x$$

The angle of elevation to the top of a radio antenna on the top of a building is \(53.4^{\circ} .\) After moving 200 feet closer to the building, the angle of elevation is \(64.3^{\circ} .\) Find the height of the building if the height of the antenna is 180 feet.

In Exercises I to \(42,\) verify each identity. $$\tan x+\cot x=\sec x \csc x$$

Solve each equation, where \(0^{\circ} \leq x<360^{\circ} .\) Round approximate solutions to the nearest tenth of a degree. $$3 \tan ^{2} x-2 \tan x=0$$

Perform the indicated operations where \(u=3 i-2 j\) and \(v=-2 i+3 j\). $$\|\mathbf{u}-2 \mathbf{v}\|$$

Find the exact value of the given expression. If an exact value cannot be given, give the value to the nearest ten-thousandth. $$\tan ^{-1}\left(\sin \frac{\pi}{6}\right)$$