Find exact values of the inverse trigonometric functions or relations.
Arcsec $2$

Evaluate the given expression, leaving the answer in simple radical form. Note that the expression $\sin ^2 \theta$ means $(\sin \theta)^2$.\

$$\cos 45^{\circ} \sin 210^{\circ}-\sin 30^{\circ} \cos 135^{\circ}$$

Evaluate the given expression, leaving the answer in simple radical form. Note that the expression $\sin ^2 \theta$ means $(\sin \theta)^2$.\

$$20 \sin 60^{\circ} \cos 240^{\circ}$$

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

$$\operatorname{Sin}^{-1} 1$$

Evaluate the given expression, leaving the answer in simple radical form. Note that the expression $\sin ^2 \theta$ means $(\sin \theta)^2$.\

$$12 \sin 45^{\circ} \cos 45^{\circ}$$

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

$$\operatorname{arccot}(-1)$$

Find the argument $x$ (between $0$ and $\frac{\pi}{2}$ ). Round to $4$ decimal places.\

$$x=\sin ^{-1} 0.3651$$

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

$$\operatorname{Cos}^{-1} 1$$

Evaluate the given expression, leaving the answer in simple radical form. Note that the expression $\sin ^2 \theta$ means $(\sin \theta)^2$.\

$$\sin 300^{\circ} \csc 300^{\circ}$$

Find and sketch the reference angle for $253^{\circ}$.

For $y=2+3 \cos 4(x-5)$, what is the:
phase displacement?

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.\

$$y=\cos \theta$$

arzan Problem Tarzan is swinging back and forth on his grapevine. As he swings, he goes back and forth across the river bank, going alternately over land and water Jane decides to mathematically model his motion and starts her stopwatch.
Let $t$ be the number of meters Tarzan is from the river bank. Assume that $y$ varies sinusoidally with $t$ and that $y$ is positive when Tarzan is over water and negative when he is over land.
Jane finds that when $t=2$, Tarzan is at one end of his swing, where $y=-23$. She finds that when $t=5$ he reaches the other end of his swing and $y=17$.
a. Sketch a graph of this sinusoidal function.
b. Write the particular equation expressing Tarzan's distance from the river bank in terms of $t$.
c. Predict $y$ when
i. $t=2.8$,
ii. $t=6.3$,
iii. $t=15$.
d. Where was Tarzan when Jane started the stopwatch?

Find the period: $y=3 \cos x$