Calculus I                                                                       Quiz #3                              September 16, 2002

Name____________________                              R.  Hammack                                     Score ______

(1) In this problem, [Graphics:Images/quiz3_gr_1.gif]   and   [Graphics:Images/quiz3_gr_2.gif].

(a)   [Graphics:Images/quiz3_gr_3.gif] [Graphics:Images/quiz3_gr_4.gif]

(b)   [Graphics:Images/quiz3_gr_5.gif][Graphics:Images/quiz3_gr_6.gif][Graphics:Images/quiz3_gr_7.gif]

You can simplify the above answer further, but don't forget to FOIL!!   

(2)  Find the equation of the line that passes through the points [Graphics:Images/quiz3_gr_12.gif] and [Graphics:Images/quiz3_gr_13.gif]. Please put your final answer in slope-intercept form, and simplify as much as possible.

slope = m = [Graphics:Images/quiz3_gr_14.gif]= -3

Using the fact we know the line has slope -3 and passes through the point (3,1), the point-slope formula gives

(a)   [Graphics:Images/quiz3_gr_18.gif][Graphics:Images/quiz3_gr_19.gif]

(b)  Find all solutions of the equation   [Graphics:Images/quiz3_gr_20.gif].  Please support your work with a picture involving the unit circle.
For x to be a solution of this equation, the point x on the unit circle must have a y-coordinate of -1/2. The two such points with radian measure between 0 and 2π are [Graphics:Images/quiz3_gr_21.gif]amd [Graphics:Images/quiz3_gr_22.gif]
The solutions of the equation are thus [Graphics:Images/quiz3_gr_23.gif], where n is an integer.