SOLUTION: Solve cos^2(w)=-3sin(w) for all solutions 0 <= w < 2pi

Algebra ->  Trigonometry-basics -> SOLUTION: Solve cos^2(w)=-3sin(w) for all solutions 0 <= w < 2pi      Log On


   

Question 799269: Solve cos^2(w)=-3sin(w) for all solutions 0 <= w < 2pi
Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
Solve cos^2(w)=-3sin(w) for all solutions 0 <= w < 2pi
cos^2(w)=-3sin(w)
1-sin^2(w)=-3sin(w)
sin^2(w)-3sin(w)-1=0
use quadratic formula to solve for sin(w)
sin%28w%29+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
a=1, b=-3, c=-1
ans:
sin(w)=-0.3028
w≈3.4492, 5.9755 (in quadrants III and IV where sin<0)
or
sin(w)=3.3028(reject, -1 < sin(w) < 1)