91Ó°ÊÓ

Convert the angle from radian measure into degree measure. $$ \frac{\pi}{2} $$

In Exercises \(43-57,\) find all of the angles which satisfy the equation. $$ \sec (\theta)=2 $$

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. \(\operatorname{arcsec}(-1)\)

In Exercises \(44-50\), graph the function with the help of your calculator and discuss the given questions with your classmates. \(f(x)=\cos (3 x)+\sin (x)\). Is this function periodic? If so, what is the period?

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

Use the Half Angle Formulas to find the exact value. You may have need of the Quotient, Reciprocal or Even / Odd Identities as well. \(\sin \left(\frac{\pi}{12}\right)\) (compare with Exercise 18)

In Exercises \(43-58\), solve the equation, giving the exact solutions which lie in \([0,2 \pi)\). $$ \cos (2 x) \cos (x)+\sin (2 x) \sin (x)=1 $$

In Exercises \(43-57,\) find all of the angles which satisfy the equation. $$ \csc (\theta)=-1 $$

Graph the function with the help of your calculator and discuss the given questions with your classmates. \(f(x)=\frac{\sin (x)}{x}\). What appears to be the horizontal asymptote of the graph?

In Exercises \(43-57,\) find all of the angles which satisfy the equation. $$ \cot (\theta)=\frac{\sqrt{3}}{3} $$