SOLUTION: If sin theta=5/12, determine sin2theta, where theta is in the first quadrant.

Algebra ->  Trigonometry-basics -> SOLUTION: If sin theta=5/12, determine sin2theta, where theta is in the first quadrant.      Log On


   

Question 1189410: If sin theta=5/12, determine sin2theta, where theta is in the first quadrant.
Answer by ikleyn(52832) About Me  (Show Source):
You can put this solution on YOUR website!
.
If sin theta=5/12, determine sin2theta, where theta is in the first quadrant.
~~~~~~~~~~~~~~ 

Use the basic formula of Trigonometry

    sin%282theta%29 = 2sin%28theta%29%2Acos%28theta%29.


From this formula, you see that you need to know cos%28theta%29.


It is easy to calculate  cos%28theta%29  from  sin%28theta%29

    cos%28theta%29 = sqrt%281-sin%5E2%28theta%29%29 = sqrt%281+-+%285%2F12%29%5E2%29 = sqrt%281-25%2F144%29 = sqrt%28%28144-25%29%2F144%29 = sqrt%28119%2F144%29 = sqrt%28119%29%2F12.


In the first quadrant, cosine is positive; therefore, we keep the positive sign of the square root.


Now  sin%282theta%29 = 2sin%28theta%29%2Acos%28theta%29 = 2%2A%285%2F12%29%2A%28sqrt%28119%29%2F12%29 = %2810%2F144%29%2Asqrt%28119%29 = 0.757549...   ANSWER

Solved.

------------------

P.S.   My inner voice tells me that should be   sin%28theta%29 = 5%2F13   in your post,  instead of  5%2F12.

If it is so,  do everything the same.  In this case the answer is   sin%282theta%29 = 2%2A%285%2F13%29%2A%2812%2F13%29 = 120%2F169.