Question #34897

1 Answer
Nghi N.
Mar 19, 2017

#+- 68^@28 + k360^@#

Explanation:

Solve this quadratic equation for cos x by using the improved quadratic formula (Socratic Search)
#2cos^2 x + 2cos x - 1 = 0#
#D = d^2 = b^2 - 4ac = 4 + 8 = 12# --> #d = +- 2sqrt3#
There are 2 real roots:
#cos x = -b/(2a) +- d/(2a) = - 1/2 +- sqrt3/2 = (-1 +- sqrt3)/2#
2 solutions for cos x:
#cos x = (-1 + sqrt3)/2 = 0.73/2 = 0.37#, and
#cos x = (- 1 - sqrt3)/2 = -2.73/2 = - 1.37# (Rejected as < - 1)
Use unit circle and calculator:
#cos x = 0.37# --> #x = +- 68^@28 + k360^@#

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