SOLUTION: Hello, I have to find a trig equation for all the values of theta (0< x < 2pi) (< = less than or equal to). The problem is 7cos^2theta-1 = 5costheta. I got .88 and -.16 but thos

Algebra ->  Trigonometry-basics -> SOLUTION: Hello, I have to find a trig equation for all the values of theta (0< x < 2pi) (< = less than or equal to). The problem is 7cos^2theta-1 = 5costheta. I got .88 and -.16 but thos      Log On


   

Question 966067: Hello,
I have to find a trig equation for all the values of theta (0< x < 2pi) (< = less than or equal to). The problem is 7cos^2theta-1 = 5costheta. I got .88 and -.16 but those answers are wrong. Any help would be greatly appreciated. Thanks!
K.Legters
Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
7cos^2theta-1 = 5costheta
7cos^2(x)-1 = 5cosx
solve for cos x using quadratic formula:
7cos^2(x)-5cosx-1=0
cosx+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
a=7,b=-5, c=-1
ans:cosx+=+%285+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
a=7,b=-5, c=-1
ans:cosx+=+%285+%2B-+sqrt%28+25%2B28+%29%29%2F%2814%29+
cosx+=+%285+%2B-+sqrt%28+53+%29%29%2F%2814%29+
cosx=0.877
x=0.50, 5.78(In quadrants I and IV where cos>0)
or
cosx=-0.16
x=1.73, 4.55 (In quadrants II and III where cos<0)