MTH 120 — Summer — 2005
Essex County College — Division of Mathematics
Quiz # 81— Printed June 9, 2005
Name:
Signature:
Show all work clearly and in order, and box your final answers . Justify your answers alge-
braically whenever possible. You have 20 minutes to take this 10 point quiz. When you do use
your calculator, sketch all relevant graphs and write down all relevant mathematics.
1. Solve for x.
(a) sin x+√2 = −sin xin the interval [0,2π).
Solution:
sin x+√2 = −sin x
2 sin x=−√2
sin x=−
√2
2.
The reference is 45◦and the solutions occur in the third and fourth quadrant, so
x= 45◦+ 180◦= 225◦=5π
4and x= 360◦
−45◦= 315◦=7π
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(b) 2 sin2x−sin x−1 = 0 in the interval [0,2π).
Solution:
2 sin2x−sin x−1=0
(2 sin x+ 1) (sin x−1) = 0.
Which gives two equations to solve.
sin x=−
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2and sin x= 1.
The reference for the first equation is 30◦and the solutions occur in the third and
fourth quadrant, so
x= 30◦+ 180◦= 210◦=7π
6and x= 360◦
−30◦= 330◦=11π
6,
and the solution to the second equation is x=π
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1This document was prepared by Ron Bannon using L
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