SOLUTION: Hi-- I am really struggling with this problem. I can't seem to get the right answer. If you could help me, that would be greatly appreciated. Thanks! :) Find sin theta/2, given

Question 189614: Hi-- I am really struggling with this problem. I can't seem to get the right answer. If you could help me, that would be greatly appreciated. Thanks! :)
Find sin theta/2, given that sin theta=1/4, and theta terminates in quadrant I.
Answer Options:
A. sqrt (8+2sqrt15 /4)
B. sqrt (8-2sqrt15 /4)
C. sqrt (6) / 4
D. sqrt (10) / 4
I have tried this problem, but this is what I got:
sin theta = 1/4, theta lies in Quadrant I
sin theta/2 = √[(1-cos theta)/2]
since sin theta = 1/4, then cos theta = √15/ 4.
sin theta/2 = √([1 - √15/4]/ 2) = √[(4 - √15)/8] = [√2(4-√15)]/4 : This is not one of my answer choices.
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
Find sin theta/2, given that sin theta=1/4, and theta terminates in quadrant I.
Answer Options:
A. sqrt (8+2sqrt15 /4)
B. sqrt (8-2sqrt15 /4)
C. sqrt (6) / 4
D. sqrt (10) / 4
I have tried this problem, but this is what I got:
sin theta = 1/4, theta lies in Quadrant I
sin theta/2 = √[(1-cos theta)/2]
since sin theta = 1/4, then cos theta = √15/4
sin theta/2 = √([1 - √15/4]/ 2) = √[(4 - √15)/8] = [√2(4-√15)]/4 : This is not one of my answer choices.
------------------
since sin theta = 1/4, then cos theta = √15/4
sin(t/2) =
-----------------
=
---------------
=
=
=
That's choice B, except the 4 is outside the radical.

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