91Ó°ÊÓ

The carrier wave for a certain FM radio station can be modeled by the equation \(y=A \sin \left(10^{7} \cdot 2 \pi t\right),\) where \(A\) is the amplitude of the wave and \(t\) is the time in seconds. Determine the period of the carrier wave.

Explain why the equation \(\sec \theta=0\) has no solutions.

Verify that each of the following is an identity. \(\sin \theta(\sin \theta+\csc \theta)=2-\cos ^{2} \theta\)

Find the exact value of each function. $$ \sin 390^{\circ} $$

Verify that each of the following is an identity. \(\frac{\sec \theta}{\tan \theta}=\csc \theta\)

A company estimates that it costs \(0.03 x^{2}+4 x+1000\) dollars to produce \(x\) units of a product. Find an expression for the average cost per unit.

Find the exact value of each expression. \(\cos \left(-300^{\circ}\right)\)

Find the amplitude, if it exists, and period of each function. Then graph each function. (Lesson \(14-1 )\) \(y=\csc 2 \theta\)

Find the exact value of each function. $$ \sin \left(-315^{\circ}\right) $$

Computer games often use transformations to distort images on the screen. In one such transformation, an image is rotated counterclockwise using the equations \(x^{\prime}=x \cos \theta-y \sin \theta\) and \(y^{\prime}=x \sin \theta+y \cos \theta\) . If the coordinates of an image point are \((3,4)\) after a \(60^{\circ}\) rotation, what are the coordinates of the preimage point?