Find the exact value of the given expression.

$1-2 \sin ^{2} \frac{7 \pi}{12}$.

Find the exact value of the given expression.

$\cos ^{2} \frac{\pi}{12}-\sin ^{2} \frac{\pi}{12}$.

Find the exact value of the expression.

cos 15 degrees

Solve each inequality for $0 \leq x<2 \pi$. Give answers to the nearest hundredth. You may wish to use a graphing calculator or computer.

$2 \cos x \leq \cos \left(x-\frac{\pi}{2}\right)$.

Find the two supplementary angles formed by the line 3x + 2y = 5 and the line 4x - 3y = 1

Find the exact value of the given expression.

$\frac{2 \tan \frac{\pi}{8}}{1-\tan ^{2} \frac{\pi}{8}}$.

Solve each inequality for $0 \leq x<2 \pi$. Give answers to the nearest hundredth. You may wish to use a graphing calculator or computer.

$\sin \left(3 x-\frac{\pi}{2}\right)>0$.

Find the exact value of the expression.

cos 75 degrees

Find the exact value of the given expression.

$2 \cos ^{2} \frac{\pi}{8}-1$.

Find the two supplementary angles formed by the line y = 3x - 5 and the line y = x + 4.

Evaluate tan 15 degrees and tan 105 degrees without using a calculator or tables.

Solve each inequality for $0 \leq x<2 \pi$. Give answers to the nearest hundredth. You may wish to use a graphing calculator or computer.

$$\tan x<2 \sin x$$

Simplify the given expression.

$\sqrt{\frac{1+\cos 70^{\circ}}{2}}$.

Translate the graph of y = cos x to the left by $\frac{\pi}{2}$ units, and then reflect this curve about the x-axis. What graph results?