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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,