91Ó°ÊÓ

Solve each equation for \(x\) in the given interval. Give answers exactly, if possible. Otherwise, give answers accurate to three significant figures. $$2 \sin ^{2} x-\cos x=1,0 \leqslant x<2 \pi$$

Solve each equation for \(x\) in the given interval. Give answers exactly, if possible. Otherwise, give answers accurate to three significant figures. $$\sec ^{2} x=8 \cos x,-\pi

Solve each equation for \(x\) in the given interval. Give answers exactly, if possible. Otherwise, give answers accurate to three significant figures. $$2 \cos x+\sin 2 x=0,-180^{\circ}

Solve each equation for \(x\) in the given interval. Give answers exactly, if possible. Otherwise, give answers accurate to three significant figures. $$2 \sin x=\cos 2 x, 0

Solve each equation for \(x\) in the given interval. Give answers exactly, if possible. Otherwise, give answers accurate to three significant figures. $$\cos 2 x=\sin ^{2} x, 0

Solve each equation for \(x\) in the given interval. Give answers exactly, if possible. Otherwise, give answers accurate to three significant figures. $$2 \sin x \cos x+1=0,0 \leqslant x<2 \pi$$

Solve each equation for \(x\) in the given interval. Give answers exactly, if possible. Otherwise, give answers accurate to three significant figures. $$\cos ^{2} x-\sin ^{2} x=-\frac{1}{2}, 0 \leqslant x \leqslant \pi$$

Solve each equation for \(x\) in the given interval. Give answers exactly, if possible. Otherwise, give answers accurate to three significant figures. $$\sec ^{2} x-\tan x-1=0,0 \leqslant x<2 \pi$$

Solve each equation for \(x\) in the given interval. Give answers exactly, if possible. Otherwise, give answers accurate to three significant figures. $$\tan 2 x+\tan x=0,0 \leq x<2 \pi$$

Solve each equation for \(x\) in the given interval. Give answers exactly, if possible. Otherwise, give answers accurate to three significant figures. Find an identity for \(\sin 3 x\) in terms of \(\sin x\)