SOLUTION: If cot theta = -3/4 and cos theta > 0, find sin theta. 1) -4/5 2) -3/5 3) 3/5 4) 4/5 Please show work so I can understand how to do this thank you

Algebra ->  Trigonometry-basics -> SOLUTION: If cot theta = -3/4 and cos theta > 0, find sin theta. 1) -4/5 2) -3/5 3) 3/5 4) 4/5 Please show work so I can understand how to do this thank you      Log On


   

Question 732705: If cot theta = -3/4 and cos theta > 0, find sin theta.
1) -4/5
2) -3/5
3) 3/5
4) 4/5
Please show work so I can understand how to do this thank you
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
cot%28theta%29=cos%28theta%29%2Fsin%28theta%29
Let's find x=sin%28theta%29
If x=sin%28theta%29 then cos%28theta%29=sqrt%281-x%5E2%29 and
cot%28theta%29=sqrt%281-x%5E2%29%2Fx so sqrt%281-x%5E2%29%2Fx=-3%2F4
and squaring both sides we get %281-x%5E2%29%2Fx=%28-3%2F4%29%5E2 --> %281-x%5E2%29%2Fx=9%2F16
%281-x%5E2%29%2Fx%5E2=9%2F16 --> 1%2Fx%5E2-1=9%2F16 --> 1%2Fx%5E2=1%2B9%2F16 --> 1%2Fx%5E2=25%2F16 --> x%5E2=16%2F25 --> x=-4%2F5 or x=4%2F5
But since cos%28theta%29%3E0 and cot%28theta%29=cos%28theta%29%2Fsin%28theta%29=-3%2F4%3C0
sin%28theta%29%3C0 so x=highlight%28sin%28theta%29=-4%2F5%29