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June 30, 2015

Homework Help: Trig(3 all with work)

Posted by Jon on Friday, February 15, 2008 at 3:17am.

1)Find the exact value of cos 105 by using a half-angle formula.
A)sqrt 2 - sqrt 3 /2
B)-sqrt 2 - sqrt 3 /2
C)-sqrt 2 + sqrt 3 /2
D)sqrt 2 + sqrt 3 /2

cos 105
cos 105 = cos 210/2
sqrt 1 + 210/2
sqrt 1 + sqrt 3/2 /2
sqrt 2 + sqrt 3/2 which is D

2)Find the solution of sin2 theta = cos theta if 0 -< theta < 180
A)30 degrees and 90 degrees
B)30 degrees and 150 degrees
C)30 degrees, 90 degrees, 150 degrees
D)0 degrees, 90 degrees, and 150 degrees

sin2 theta = cos theta
sin2 theta - 1 = 0
(sin theta + 1)(sin theta - 1)= 0
sin theta = -1 or sin theta = 1 which is B

3)An insect population P in a certain area fluctuates with the seasons. It is estimated that P = 17,000 + 4500 sin pi(t)/52, where t is given in weeks. Determine the number of weeks it would take for the population to initially reach 20,000.
A)12 weeks
B)692 weeks
C)38 weeks
D)42 weeks

P = 17,000 + 4500 sin pi(t)/52
20,000 = 17,000 + 4500 sin pi(t)/52
3,000 = 4500 sin pi(t)/52
.666 = sin pi(t)/52
The closest thing is C

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