91Ó°ÊÓ

Use the fact that the trigonometric functions are periodic to find the exact value of each expression. Do not use a calculator. $$ \tan (15 \pi) $$

Use a calculator to find the approximate value of each expression. Round the answer to two decimal places. $$ \tan 36^{\circ} $$

According to the Old Farmer's Almanac, in Honolulu, Hawaii, the number of hours of sunlight on the summer solstice of 2018 was \(13.42,\) and the number of hours of sunlight on the winter solstice was 10.83 . (a) Find a sinusoidal function of the form $$ y=A \sin (\omega x-\phi)+B $$ that models the data. (b) Use the function found in part (a) to predict the number of hours of sunlight on April \(1,\) the 91 st day of the year. (c) Draw a graph of the function found in part (a). (d) Look up the number of hours of sunlight for April 1 in the Old Farmer's Almanac, and compare the actual hours of daylight to the results found in part (b).

Name the quadrant in which the angle \(\theta\) lies. $$ \cos \theta>0, \quad \tan \theta>0 $$

Graph each function. Be sure to label key points and show at least two cycles. Use the graph to determine the domain and the range of each function. $$ y=2 \csc \left(\frac{1}{3} x\right)-1 $$

Name the quadrant in which the angle \(\theta\) lies. $$ \csc \theta>0, \quad \cot \theta<0 $$

Convert each angle in radians to degrees. \(\frac{3 \pi}{20}\)

Use Fundamental Identities and/or the Complementary Angle Theorem to find the exact value of each expression. Do not use a calculator. $$\tan 70^{\circ}-\frac{\sin 70^{\circ}}{\cos 70^{\circ}}$$

Use Fundamental Identities and/or the Complementary Angle Theorem to find the exact value of each expression. Do not use a calculator. $$\cot 25^{\circ}-\frac{\cos 25^{\circ}}{\sin 25^{\circ}}$$

Find the reference angle of each angle. $$ 210^{\circ} $$