Question #d89db

1 Answer
Nghi N
Sep 8, 2017

pi/6; (5pi)/6

Explanation:

f(x) = 4cos^2 x - 4sin x - 1 = 0
Replace cos^2 x by (1 - sin^2 x)
4(1 - sin^2 x) - 4sin x - 1 = 0
4 - 4sin^2 x - 4sin x - 1 = 0
Change side. Solve the quadratic equation by the improved quadratic formula in graphic form (Socratic, Google Search):
4sin^2 x + 4sin x - 3 = 0
D = d^2 = b^2 - 4ac = 16 + 48 = 64 --> d = +- 8

There are 2 real roots:
sin x = - b/(2a) +- d/(2a) = - 1/2 +- 1
sin x = - 1/2 + 1 = 1/2 and sin x = - 3/2 (rejected as < - 1)
sin x = 1/2 --> trig table and unit circle give -->
x = pi/6, and x = pi - pi/6 = (5pi)/6

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