91Ó°ÊÓ

Use a calculator to evaluate each trigonometric function. Make sure that the calculator is in \(R A D I A N\) mode. $$\sin ^{-1}(-0.05)$$

Find two angles that are coterminal with it. $$210^{\circ}$$

Find the exact value of each trigonometric function. $$\csc 45^{\circ}$$

Use a scientific calculator to evaluate the trigonometric functions. Make sure the calculator is in DEGREE mode. Round to four decimal places. \(.\) tan \(17^{\circ}\)

Convert each angle from degrees to radians. $$270^{\circ}$$

Convert each angle from degrees to radians. $$390^{\circ}$$

In this set of exercises, you will use right triangle trigonometry to study real-world problems. Unless otherwise indicated, round answers to four decimal places. A 20 -foot-long piece of wire is attached to the top of a pole at one end and nailed to the ground at the other end. If the wire makes an angle of \(30^{\circ}\) with the ground, find the height of the pole.

Convert the angle measures given in DMS form to decimal degrees with three decimal places. $$25^{\circ} 45^{\prime} 15^{\prime \prime}$$

The horizontal range of a projectile that is fired with an initial velocity \(v_{0}\) at an acute angle \(\theta\) with respect to the horizontal is given by $$R=\frac{\left(v_{0}\right)^{2} \sin 2 \theta}{g}$$ where \(g\) is the gravitational constant, 9.8 meters per second per second \(\left(\mathrm{m} / \mathrm{sec}^{2}\right) .\) If \(v_{0}=30\) meters per second, find the angle at which the projectile must be fired if it is to have a horizontal range of 80 meters. Express your answers in degrees.

Using appropriate graphs, show that \(\sin (-x)=-\sin x\)