91Ó°ÊÓ

A parallelogram has sides of lengths 3 and \(5,\) and one angle is \(50^{\circ} .\) Find the lengths of the diagonals.

Two straight roads diverge at an angle of \(65^{\circ} .\) Two cars leave the intersection at \(2 : 00\) P.M. one traveling at 50 \(\mathrm{mi} / \mathrm{h}\) and the other at 30 \(\mathrm{mi} / \mathrm{h}\) . How far apart are the cars at \(2 : 30 \mathrm{P.M.?}\)

Write the first trigonometric function in terms of the second for \(\theta\) in the given quadrant. $$ \cos \theta, \quad \sin \theta ; \quad \theta \text { in Quadrant IV } $$

Find an angle between \(0^{\circ}\) and \(360^{\circ}\) that is coterminal with the given angle. $$ 1110^{\circ} $$

A car travels along a straight road, heading east for 1 h, then traveling for 30 min on another road that leads northeast. If the car has maintained a constant speed of 40 mi/h, how far is it from its starting position?

Find an angle between \(0^{\circ}\) and \(360^{\circ}\) that is coterminal with the given angle. $$ -100^{\circ} $$

Write the first trigonometric function in terms of the second for \(\theta\) in the given quadrant. $$ \sec \theta, \quad \sin \theta ; \quad \theta \text { in Quadrant } \mathrm{I} $$

Find an angle between \(0^{\circ}\) and \(360^{\circ}\) that is coterminal with the given angle. $$ -800^{\circ} $$

Surfing the Perfect Wave For a wave to be surfable, it can't break all at once. Robert Guza and Tony Bowen have shown that a wave has a surfable shoulder if it hits the shoreline at an angle \(\theta\) given by $$ \theta=\sin ^{-1}\left(\frac{1}{(2 n+1) \tan \beta}\right) $$ where \(\beta\) is the angle at which the beach slopes down and where \(n=0,1,2, \ldots\) (a) For \(\beta=10^{\circ},\) find \(\theta\) when \(n=3\) (b) For \(\beta=15^{\circ},\) find \(\theta\) when \(n=2,3,\) and \(4 .\) Explain why the formula does not give a value for \(\theta\) when \(n=0\) or 1

Write the first trigonometric function in terms of the second for \(\theta\) in the given quadrant. $$ \sec \theta, \quad \tan \theta ; \quad \theta \text { in Quadrant II } $$