In a reference book find information about two of the following:

a. the range of assigned frequencies of the FM broadcasting channels in the United States

b. the frequency ranges for VHF (very high frequency) and UHF (ultra high frequency) television

c. the frequencies of ultraviolet light and infrared light

d. the frequency of the musical pitch called "middle C ".

The initials FM stand for frequency modulation. In FM broadcasting, information is communicated by varying the frequency; that is, the constant frequency f is replaced by a variable frequency f(t), which is a function of time. An exaggerated graph of this situation appears at the right. A complication of FM broadcasting is that f(t) must remain near the radio station's assigned frequency. FM frequencies are given in MHz (millions of cycles per second).

a. Suppose that an FM radio wave has an equation of the following form: $V(t)=A \sin [2 \pi(200,000,000+10,000 \sin 500 \pi t)] t$. Thus, the varying frequency is $f(t)=200,000,000+10,000 \sin 500 \pi t$. What is the assigned frequency in $\mathrm{MHz}$ ?

b. Give the maximum and minimum frequencies of this FM radio wave over a long period of time.

Solve the equation for $0 \leq x<2 \pi$ by using a graphing calculator or computer. Give answers to the nearest hundredth of a radian.

$$\sin x=\frac{x}{2}$$

In the given exercise, prove the given identity.

$$\frac{\sin \theta}{\csc \theta}+\frac{\cos \theta}{\sec \theta}=\sin \theta \csc \theta$$

Without using tables or a calculator, solve for $0 \leq x<2 \pi$.

$$|\csc x|=1$$

In the given exercise, prove the given identity.

$$\frac{\cot \theta-\tan \theta}{\sin \theta \cos \theta}=\csc ^2 \theta-\sec ^2 \theta$$

Find the inclination of the line. Give your answers to the nearest degree.

A line parallel to 2 x+3 y=-6

An AM radio wave means that the amplitude is modulated. Thus, instead of a constant amplitude A, there is a varying amplitude A(t) as shown below. Each AM radio station in the United States is assigned a frequency between 540 kHz and 1700 kHz. (A hertz (Hz) is one cycle per second, so 1 kHz is 1000 cycles per second.)

Solve the equation for $0 \leq x<2 \pi$ by using a graphing calculator or computer. Give answers to the nearest hundredth of a radian.

$$\tan x=x$$

For the given exercise, refer to the sine wave shown. What is the axis of the wave?

Calculate the values of the following if $1+\cot ^2 \theta=\csc ^2 \theta$ :

a. $\csc ^2 \theta-1=$ ?

b. $\csc ^2 \theta-\cot ^2 \theta=$ ?

Solve 3-csc x=7 for $0 \leq x<2 \pi$. Give answers to the nearest hundredth of a radian.

For the given exercise, sketch and label the graphs given on a single set of axes.

$$y=\sin x, y=\sin \frac{1}{2} x$$

Give answers to the nearest tenth of a degree for solving $0^{\circ} \leq \theta<360^{\circ}$.

$$\tan \theta=1.2$$