91Ó°ÊÓ

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. \(\operatorname{arccsc}\left(-\frac{2 \sqrt{3}}{3}\right)\)

Graph the function with the help of your calculator and discuss the given questions with your classmates. \(f(x)=\sin \left(\frac{1}{x}\right)\). What's happening as \(x \rightarrow 0 ?\)

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

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

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

Solve the equation for \(t\). $$ \cos (t)=-\frac{\sqrt{2}}{2} $$

Sketch the oriented arc on the Unit Circle which corresponds to the given real number. $$ t=-2 $$

In Exercises \(43-58\), solve the equation, giving the exact solutions which lie in \([0,2 \pi)\). $$ \sin (x)+\sqrt{3} \cos (x)=1 $$

Use the Half Angle Formulas to find the exact value. You may have need of the Quotient, Reciprocal or Even / Odd Identities as well. $$ \tan \left(\frac{7 \pi}{8}\right) $$

Use your calculator to approximate the given value to three decimal places. $$ \sin \left(78.95^{\circ}\right) $$