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Calculus I Quiz
3 September
21, 2004

Name _________________ R. Hammack Score_____

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(1) Find the equation of the line that
passes through the point (5, 9) and has x-intercept
7.

Please express your answer in slope-intercept form.

We know 2 points on the line. (5, 9) and (7, 0). Thus
its slope is

Using the point-slope form of the equation for a line, we get

(2)

(a)
(by looking at the unit circle)

(b)
-1

(Because any radian measure that's an odd multiple of
corresponds to the point (-1, 0) on the unit circle.)

(3) Find all values of x
(in radians) for which .

From the unit circle, you can see that if ,
then tan(x) = -1.

But note also you can add any integer multiple of
to this value, and still tan(x)
= -1.

SOLUTION:

(4) Suppose x
is a number for which . What
are the possible values for ?

From the identity ,
we get ,
or .

Thus , so .

Now,