Posted by Sandy on Sunday, June 6, 2010 at 11:19pm.
solve for x if x is in radians.
cos2(x) + 4cos(x) = 3

trig  Reiny, Sunday, June 6, 2010 at 11:24pm
Is that
cos^2 x + 4cosx = 3 ??
if so, then let cosx = y to get
y^2 + 4y + 3 = 0
(y+1)(y+3) = 0
y = 1 or y = 3
so
cosx = 1 > x = π
or
cosx = 3 , not possible
so x = π

trig  Sandy, Sunday, June 6, 2010 at 11:27pm
no, its not squared. it is (cosx)(2)

trig  Reiny, Sunday, June 6, 2010 at 11:42pm
(cosx)(2) wouldn't make much sense, then it would be
2cosx and the entire equation would be
6cosx = 3
cosx = 1/2
and x = 120° or 240°
did you mean cos(2x) ?
then you can use the identity
cos(2x) = 2cos^2x  1
cos((x) + 4cos(x) = 3
2cos^2x  1 + 4cosx = 3
2cos^2x + 4cosx + 2 = 0
cos^2x + 2cosx + 1 = 0
(cosx + 1)^2 = 0
cosx + 1 = 0
cosx = 1
x = 180° or x = π
(which by coincidence is the same answer to the other interpretation)

trig  Sandy, Sunday, June 6, 2010 at 11:49pm
okay i think that is right. thank you
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