Question

Question #34897

Answer 1

`+- 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^@`