91Ó°ÊÓ

Find all of the angles which satisfy the equation. $$ \csc (\theta)=-1 $$

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

Sketch the oriented arc on the Unit Circle which corresponds to the given real number. $$ t=-\pi $$

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

Solve the equation, giving the exact solutions which lie in \([0,2 \pi)\). $$ \cos (5 x) \cos (3 x)-\sin (5 x) \sin (3 x)=\frac{\sqrt{3}}{2} $$

Graph the function with the help of your calculator and discuss the given questions with your classmates. \(f(x)=x \sin (x)\). Graph \(y=\pm x\) on the same set of axes and describe the behavior of \(f\).

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. $$ \cos \left(\frac{\pi}{8}\right) $$

In Exercises \(40-48\), solve the equation for \(t\). (See the comments following Theorem 10.5.) $$ \cos (t)=1 $$

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

Find all of the angles which satisfy the equation. $$ \tan (\theta)=0 $$