91Ó°ÊÓ

In right triangle trigonometry, explain why \(\sin 30^{\circ}=\frac{1}{2}\) regardless of the size of the triangle.

Write an equation for the function that is described by the given characteristics. A cosine curve with a period of \(\pi,\) an amplitude of \(1,\) a left phase shift of \(\pi,\) and a vertical translation down \(\frac{3}{2}\) units

Use a calculator to evaluate the trigonometric function. Round your answer to four decimal places. (Be sure the calculator is set in the correct angle mode.) $$ \tan \frac{\pi}{9} $$

Sketch a graph of the function. $$ y=2 \arccos x $$

Use a graphing utility to graph the function. Describe the behavior of the function as \(x\) approaches zero. $$ y=\frac{6}{x}+\cos x, \quad x>0 $$

Write an equation for the function that is described by the given characteristics. A cosine curve with a period of \(4 \pi\), an amplitude of 3 , a right phase shift of \(\pi / 2,\) and a vertical translation up 2 units

Use a calculator to evaluate the trigonometric function. Round your answer to four decimal places. (Be sure the calculator is set in the correct angle mode.) $$ \tan \left(-\frac{\pi}{9}\right) $$

Convert each angle measure to degrees, minutes, and seconds without using a calculator. Then check your answers using a calculator. (a) \(-345.12^{\circ}\) (b) \(0.45^{\circ}\)

Use a graphing utility to graph the function. Describe the behavior of the function as \(x\) approaches zero. $$ y=\frac{4}{x}+\sin 2 x, \quad x>0 $$

Sketch a graph of the function. $$ g(t)=\arccos (t+2) $$