91Ó°ÊÓ

In Exercises \(19-42,\) solve the equation, giving the exact solutions which lie in \([0,2 \pi)\) $$ 2 \tan (x)=1-\tan ^{2}(x) $$

Verify the identity by graphing the right and left hand sides on a calculator. \(\tan (x+\pi)=\tan (x)\)

In Exercises \(35-42,\) use your ealculator to approximate the given value to three decimal places. Make sure your calculator is in the proper angle measurement mode! $$ \cot \left(3^{\circ}\right) $$

Use the Half Angle Formulas to find the exact value. You may have need of the Quotient, Reciprocal or Even / Odd Identities as well. $$ \cos \left(67.5^{\circ}\right) $$

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. \(\operatorname{arcsec}(-2)\)

Convert the angle from radian measure into degree measure. $$ \frac{\pi}{3} $$

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

Use the Half Angle Formulas to find the exact value. You may have need of the Quotient, Reciprocal or Even / Odd Identities as well. \(\sin \left(157.5^{\circ}\right)\)

Convert the angle from radian measure into degree measure. $$ \frac{5 \pi}{3} $$

In Exercises \(19-42,\) solve the equation, giving the exact solutions which lie in \([0,2 \pi)\) $$ \tan (x)=\sec (x) $$