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(a) Which of the following figures represents a graphical solution to the equation $\tan(\theta)=6.6$ ?



A		B



C		D

(b) What is the period of the tangent function? .

(d) Note that the cosine function has period $2\pi$ and usually has two solutions on each repeated segment when solving an equation such as $\cos(\theta)=.4$ . Compare this with your answers to the previous two questions. How will these differences affect the process of solving the equation $\tan(\theta)=6.6$ ?

A. There are two solutions on each repeated segment and the period is $2\pi$ , but solutions all differ by multiples of $\pi$ , so solutions will have the form $a+\pi n$ where $a$ is an initial solution and $n$ is any integer.

B. Since there is only one solution on each repeated segment and the period is $\pi$ , solutions will have the form $a+\pi n$ where $a$ is an initial solution and $n$ is any integer.

C. Since there is only one solution on each repeated segment and the period is $2\pi$ , solutions will have the form $a+2\pi n$ where $a$ is an initial solution and $n$ is any integer.

D. Since there are two solutions on each repeated segment and the period is $\pi$ , solutions will have the form $a+\pi n$ and where $a$ is an initial solution and $n$ is any integer.

(e) Find all solutions to $\tan(\theta)=6.6$ .

$\theta =$ + $n$

where the initial solution is between $-\frac{\pi}{2}$ and $\frac{\pi}{2}$ , and $n$ is any integer. Use radian measure and enter your answers using at least four significant digits.

Hint: