Find exact values of the inverse circular functions or relations.\

$$\arctan 1$$

Sketch quickly two complete cycles of the trigonometric or circular function graph. Do this by locating critical features such as high or low points and asymptotes. After you have sketched the graph, look back at this section to make sure you are correct. If not, then redraw your graphs.\

$$y=\csc x$$

Suppose that $y=4+2 \sec 3\left(\theta+20^{\circ}\right)$.
a. Transform the equation so that $\theta$ is expressed in terms of $y$.
b. Find the least positive value of $\theta$ for which
i. $y=6$,
ii. $y=3$,
iii. $y=0$.
c. Show that your answers are right by sketching the graph.

Find the indicated function value. Round to four significant digits.\

$$\tan 85^{\circ} 18^{\prime}$$

Sketch quickly two complete cycles of the trigonometric or circular function graph. Do this by locating critical features such as high or low points and asymptotes. After you have sketched the graph, look back at this section to make sure you are correct. If not, then redraw your graphs.\

$$y=\tan x$$

Find the exact values of the six circular functions of the given argument.\

$$-\pi$$

Sketch the graph of the indicated trigonometric or circular function. You may use different scales on the horizontal and vertical axes, if necessary, to make the graphs have reasonable proportions.\

$$y=-6+7 \sin \frac{\pi}{4}(x-2)$$

Sketch the graph of the indicated trigonometric or circular function. You may use different scales on the horizontal and vertical axes, if necessary, to make the graphs have reasonable proportions.\

$$y=3+5 \sin \frac{\pi}{4}(x-3)$$

Sketch quickly two complete cycles of the trigonometric or circular function graph. Do this by locating critical features such as high or low points and asymptotes. After you have sketched the graph, look back at this section to make sure you are correct. If not, then redraw your graphs.\

$$y=\cot x$$

Suppose that $y=2+\frac{1}{2} \tan \frac{\pi}{4}(x-0.6)$.
a. Transform the equation so that $x$ is expressed in terms of $y$.
b. Find the smallest positive value of $x$ for which
i. $y=2.5$,
ii. $y=0$.
c. Show that your answers are right by sketching the graph.

Find the exact values of the six circular functions of the given argument.\

$$\frac{-5 \pi}{2}$$

Find the indicated function value. Round to four significant digits.\

$$\cot 17^{\circ} 4^{\prime}$$

Derive equations expressing Arccot $x$ and Arcsec $x$ in terms of Arctangents.

Show that there is a very easy way to find Arccsc $x$ in terms of an Arcsine. Then use the results to write an equation expressing Arcsec $x$ as an Arctangent function.