91Ó°ÊÓ

If \(\sin \theta=x\) and \(\theta\) is in quadrant IV, find an expression for \(\sec \theta\) in terms of \(x\).

Verify that each equation is an identity. $$\frac{1+\cos 2 x}{\sin 2 x}=\cot x$$

Draw by hand the graph of each inverse function. $$y=\csc ^{-1} x$$

Verify that each equation is an identity. $$\frac{\cos (A-B)}{\sin (A+B)}=\frac{1+\cot A \cot B}{\cot A+\cot B}$$

Verify that each equation is an identity. $$\sec ^{2} \frac{x}{2}=\frac{2}{1+\cos x}$$

]Give solutions over the interval \([0,2 \pi)\) as approximations to the nearest hundredth when exact values cannot be determined. You may need to use the quadratic formula. Give approximate answers in Exercises \(59-64\) to the nearest tenth of a degree over the interval \(\left[0^{\circ}, 360^{\circ}\right)\) $$2 \sin \theta=1-2 \cos \theta$$

Perform indicated operation and simplify the result. $$\cot \theta+\frac{1}{\cot \theta}$$

Verify that each equation is an identity. $$\sec 2 x=\frac{1+\tan ^{2} x}{1-\tan ^{2} x}$$

Give solutions over the interval \([0,2 \pi)\) as approximations to the nearest hundredth when exact values cannot be determined. You may need to use the quadratic formula. Give approximate answers in Exercises \(59-64\) to the nearest tenth of a degree over the interval \(\left[0^{\circ}, 360^{\circ}\right)\) $$\sin ^{2} \theta-\cos \theta=0$$

Perform indicated operation and simplify the result. $$\frac{\sec x}{\csc x}+\frac{\csc x}{\sec x}$$