SOLUTION: If sin theta = -5/13 and theta terminates in 3rd quadrant find cos theta and tan theta.

Algebra ->  Trigonometry-basics -> SOLUTION: If sin theta = -5/13 and theta terminates in 3rd quadrant find cos theta and tan theta.      Log On


   

Question 1061978: If sin theta = -5/13 and theta terminates in 3rd quadrant find cos theta and tan theta.
Found 2 solutions by ikleyn, MathTherapy:
Answer by ikleyn(52799) About Me  (Show Source):
You can put this solution on YOUR website!
.
If sin theta = -5/13 and theta terminates in 3rd quadrant find cos theta and tan theta.
~~~~~~~~~~~~~~~~~ 

In QIII  cos%28theta%29 = -sqrt%281-sin%5E2%28theta%29%29 = -sqrt%281-%28-5%2F13%29%5E2%29 = -sqrt%281-25%2F169%29 = -sqrt%28%28169-25%29%2F169%29 = -sqrt%28144%2F169%29 = -12%2F13.


Then   tan%28theta%29 = sin%28theta%29%2Fcos%28theta%29%29 = %28%28-5%2F13%29%29%2F%28%28-12%2F13%29%29 = 5%2F12.

Solved.


Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!

If sin theta = -5/13 and theta terminates in 3rd quadrant find cos theta and tan theta.
sin+%28theta%29+=+%28-+5%29%2F13+=+O%2FH+=+y%2Fr

With y = - 5, and r = 13, we have a 5-12-13 Pythag-triple triangle

Therefore, x MUST = - 12 (x is NEGATIVE in 3rd quadrant)