Expert: Paul Klarreich - 9/27/2008

Question
Q1:Find cos theta/2 given that sin theta=-12/13 and theta is in fourth quadrant?

Q:Find sin theta/2 given that sin theta=-5/13 and theta is in third quadrant?
I need answers  in detail.Thank you

Answer
Questioner:   ahmed
Category:  Advanced Math
Private:  No
 
Subject:  trigonometry
Question:  Q1:Find cos theta/2 given that sin theta=-12/13 and theta is in fourth quadrant?

Q:Find sin theta/2 given that sin theta=-5/13 and theta is in third quadrant?
I need answers in detail.Thank you
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Hi, Ahmed,

I'll work on the first one and leave the second to you.

If  sin t = -12/13, and  t is in Q4, then take  y = -12,  r = 13, and get  r = 5 in Q4.

Now cos t/2 = +- sqrt((1 + cos t)/2).

cos t = 5/13 in Q4.

cos t/2 = +- sqrt((1 + 5/13)/2)

cos t/2 = +- sqrt((18/13)/2)

cos t/2 = +- sqrt(9/13)

You can resolve the +- only by knowing the quadrant of  t/2, which depends on the actual measure of t.

[For example,  t = 300 deg and t = -60 are both in Q4, but t/2 = 150 is in Q2 and t/2 = -30 is in Q4]