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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