91Ó°ÊÓ

Draw each of the following angles in standard position, and find one positive angle and one negative angle that is coterminal with the given angle. $$ -150^{\circ} $$

Compute the complement and supplement of \(61^{\circ}\). a. Complement \(=-61^{\circ}\), supplement \(=119^{\circ}\) b. Complement \(=-61^{\circ}\), supplement \(=299^{\circ}\) c. Complement \(=119^{\circ}\), supplement \(=29^{\circ}\) d. Complement \(=29^{\circ}\), supplement \(=119^{\circ}\)

Draw \(45^{\circ}\) and \(-45^{\circ}\) in standard position and then show that \(\cos \left(-45^{\circ}\right)=\cos 45^{\circ}\).

Draw each of the following angles in standard position, and find one positive angle and one negative angle that is coterminal with the given angle. $$ -330^{\circ} $$

Draw \(45^{\circ}\) and \(-45^{\circ}\) in standard position and then show that \(\sin \left(-45^{\circ}\right)=-\sin 45^{\circ}\).

Show that each of the following statements is an identity by transforming the left side of each one into the right side. $$ \frac{\csc \theta \tan \theta}{\sec \theta}=1 $$

In right triangle \(A B C\), find \(b\) if \(a=2, c=5\), and \(C=90^{\circ}\). a. 7 b. 3 c. \(\sqrt{21}\) d. \(\sqrt{29}\)

Show that each of the following statements is an identity by transforming the left side of each one into the right side. $$ \sin \theta \tan \theta+\cos \theta=\sec \theta $$

Find the remaining sides of a \(30^{\circ}-60^{\circ}-90^{\circ}\) triangle if the longest side is 6 . a. \(6,6 \sqrt{2}\) b. \(3 \sqrt{2}, 3 \sqrt{2}\) c. \(3,3 \sqrt{3}\) d. \(12,6 \sqrt{3}\)

Find \(y\) if the point \((5, y)\) is on the terminal side of \(\theta\) and \(\cos \theta=\frac{5}{13}\).