91Ó°ÊÓ

Express the exact value of each function as a single fraction. Do not use a calculator. $$ \text { If } \theta \text { is an acute angle and } \cos \theta=\frac{1}{3}, \text { find } \csc \left(\frac{\pi}{2}-\theta\right) $$

use reference angles to find the exact value of each expression. Do not use a calculator. $$ \tan \frac{9 \pi}{2} $$

In Exercises \(71-74,\) find the length of the arc on a circle of radius \(r\) intercepted by a central angle \(\theta .\) Express arc length in terms of \(\pi .\) Then round your answer to two decimal places. $$Radius, r \quad Central Angle, \theta$$ $$8 feet \quad \theta=225^{\circ}$$

Determine whether each statement makes sense or does not make sense, and explain your reasoning. The bearing from \(O\) to \(A\) is \(N 103^{\circ} \mathrm{W}\).

Graph \(f, g,\) and \(h\) in the same rectangular coordinate system for \(0 \leq x \leq 2 \pi .\) Obtain the graph of \(h\) by adding or subtracting the corresponding \(y\)-coordinates on the graphs of \(f\) and \(g\) $$f(x)=\sin x, g(x)=\cos 2 x, h(x)=(f-g)(x)$$

use reference angles to find the exact value of each expression. Do not use a calculator. $$ \sin \left(-240^{\circ}\right) $$

a. Graph the restricted secant function, \(y=\sec x,\) by restricting \(x\) to the intervals \(\left[0, \frac{\pi}{2}\right)\) and \(\left(\frac{\pi}{2}, \pi\right]\) b. Use the horizontal line test to explain why the restricted secant function has an inverse function. c. Use the graph of the restricted secant function to graph \(y=\sec ^{-1} x\).

At a certain time of day, the angle of elevation of the Sun is 40°. To the nearest foot, find the height of a tree whose shadow is 35 feet long.

Graph \(f, g,\) and \(h\) in the same rectangular coordinate system for \(0 \leq x \leq 2 \pi .\) Obtain the graph of \(h\) by adding or subtracting the corresponding \(y\)-coordinates on the graphs of \(f\) and \(g\) $$f(x)=\cos x, g(x)=\sin 2 x, h(x)=(f-g)(x)$$

In Exercises \(71-74,\) find the length of the arc on a circle of radius \(r\) intercepted by a central angle \(\theta .\) Express arc length in terms of \(\pi .\) Then round your answer to two decimal places. $$Radius, r \quad Central Angle, \theta$$ $$9 yards \quad \theta=315^{\circ}$$