91Ó°ÊÓ

In Exercises \(41-48\), assume that the range of arcsecant is \(\left[0, \frac{\pi}{2}\right) \cup\left[\pi, \frac{3 \pi}{2}\right)\) and that the range of arccosecant is \(\left(0, \frac{\pi}{2}\right] \cup\left(\pi, \frac{3 \pi}{2}\right]\) when finding the exact value. $$ \operatorname{arcsec}(-\sqrt{2}) $$

Solve the equation, giving the exact solutions which lie in \([0,2 \pi)\). $$ \tan (x)=\sec (x) $$

Use your calculator to approximate the given value to three decimal places. Make sure your calculator is in the proper angle measurement mode! $$ \sec (0.45) $$

Verify the identity by graphing the right and left hand sides on a calculator. $$ \sin (2 x)=2 \sin (x) \cos (x) $$

Convert the angle from radian measure into degree measure. $$ -\frac{\pi}{6} $$

In Exercises \(41-48\), assume that the range of arcsecant is \(\left[0, \frac{\pi}{2}\right) \cup\left[\pi, \frac{3 \pi}{2}\right)\) and that the range of arccosecant is \(\left(0, \frac{\pi}{2}\right] \cup\left(\pi, \frac{3 \pi}{2}\right]\) when finding the exact value. $$ \operatorname{arcsec}\left(-\frac{2 \sqrt{3}}{3}\right) $$

Solve the equation, giving the exact solutions which lie in \([0,2 \pi)\). $$ \sin (6 x) \cos (x)=-\cos (6 x) \sin (x) $$

Find all of the angles which satisfy the equation. $$ \tan (\theta)=\sqrt{3} $$

In Exercises \(39-48\), use the Half Angle Formulas to find the exact value. You may have need of the Quotient, Reciprocal or Even / Odd Identities as well. $$ \tan \left(112.5^{\circ}\right) $$

Verify the identity by graphing the right and left hand sides on a calculator. $$ \tan \left(\frac{x}{2}\right)=\frac{\sin (x)}{1+\cos (x)} $$