91Ó°ÊÓ

Determine the quadrant in which each angle lies. (The angle measure is given in radians.) (a) \(\frac{\pi}{4}\) (b) \(\frac{5 \pi}{4}\)

Evaluate (if possible) the sine, cosine, and tangent of the real number. $$ t=\frac{\pi}{4} $$

Evaluate the expression without using a calculator. $$ \arcsin \frac{\sqrt{2}}{2} $$

Find the period and amplitude. $$ y=\frac{2}{3} \cos \frac{\pi x}{10} $$

Sketch a right triangle corresponding to the trigonometric function of the acute angle \(\boldsymbol{\theta}\). Use the Pythagorean Theorem to determine the third side and then find the other five trigonometric functions of \(\boldsymbol{\theta}\). $$ \sec \theta=\frac{17}{7} $$

The point is on the terminal side of an angle in standard position. Determine the exact values of the six trigonometric functions of the angle. $$ \left(3 \frac{1}{2},-7 \frac{3}{4}\right) $$

Evaluate (if possible) the sine, cosine, and tangent of the real number. $$ t=\frac{\pi}{3} $$

Determine the quadrant in which each angle lies. (The angle measure is given in radians.) (a) \(\frac{11 \pi}{8}\) (b) \(\frac{9 \pi}{8}\)

Evaluate the expression without using a calculator. $$ \tan ^{-1}\left(-\frac{\sqrt{3}}{3}\right) $$

Sketch a right triangle corresponding to the trigonometric function of the acute angle \(\boldsymbol{\theta}\). Use the Pythagorean Theorem to determine the third side and then find the other five trigonometric functions of \(\boldsymbol{\theta}\). $$ \cot \theta=3 $$