91Ó°ÊÓ

Prove that the area of a circular sector of radius \(r\) with central angle \(\theta\) is $$A=\frac{1}{2} \theta r^{2}$$ where \(\theta\) is measured in radians.

Analyzing a Trigonometric Graph In Exercises \(77-82,\) use a graphing utility to graph the function. Describe the behavior of the function as \(x\) approaches zero. $$g(x)=\frac{\sin x}{x}$$

Using a Calculator In Exercises \(75-90\) , use a calculator to evaluate the trigonometric function. Round your answer to four decimal places. (Be sure the calculator is in the correct mode.) $$ \tan 304^{\circ} $$

True or False? In Exercises \(79-84\) , determine whether the statement is true or false. Justify your answer. $$\sin 60^{\circ} \csc 60^{\circ}=1$$

Using a Calculator In Exercises \(75-90\) , use a calculator to evaluate the trigonometric function. Round your answer to four decimal places. (Be sure the calculator is in the correct mode.) $$ \cot 178^{\circ} $$

Complete the equation. \(\arccos \frac{x-2}{2}=\arctan (\quad), \quad 2< x<4\)

Analyzing a Trigonometric Graph In Exercises \(77-82,\) use a graphing utility to graph the function. Describe the behavior of the function as \(x\) approaches zero. $$f(x)=\frac{1-\cos x}{x}$$

True or False?determine whether the statement is true or false. Justify your answer. $$\sec 30^{\circ}=\csc 60^{\circ}$$

Sketch a graph of the function and compare the graph of \(g\) with the graph of \(f(x)=\arcsin x .\) \(g(x)=\arcsin (x-1)\)

Analyzing a Trigonometric Graph In Exercises \(77-82,\) use a graphing utility to graph the function. Describe the behavior of the function as \(x\) approaches zero. $$f(x)=\sin \frac{1}{x}$$