SOLUTION: solve the equation in Radians for all exact solutions where appropriate. Round approximate answer in radians to four decimal place. write answer using the least possible non-negati

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Question 805646: solve the equation in Radians for all exact solutions where appropriate. Round approximate answer in radians to four decimal place. write answer using the least possible non-negative angle measures.

cos x (5 cos x - 1) = 3

Answer by lwsshak3(11628) About Me  (Show Source):
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solve the equation in Radians for all exact solutions where appropriate. Round approximate answer in radians to four decimal place. write answer using the least possible non-negative angle measures.
cos x (5 cos x - 1) = 3
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cos x (5 cos x - 1) = 3
5cos^2(x)-cos(x)=3
5cos^2(x)-cos(x)-3=0
solve for cos(x) by quadratic formula:
cos%28x%29+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
a=5, b=-1, c=-3
ans:
cos(x)=-0.6810
use calculator inverse cos key set to radians
x=2.3199+2πk, 3.9633,+2πk, k=integer (In quadrants II and III where cos<0)
or
cos(x)=0.8810
use calculator inverse cos key set to radians
x=0.4928+2πk, 5.7904,+2πk, k=integer (In quadrants I and IV where cos>0)