How do you solve 2sin^2 2x+4sin2x=3.759?

1 Answer
Nghi N.
Aug 30, 2015

Solve 2sin^2 x + 4sin 2x = 3.759

Ans: x = 22.22 and x = 67.78 deg

Explanation:

Call sin 2x = t. We get a quadratic equation:
2t^2 + 4t - 3.759 = 0
D = d^2 = b^2 - 4ac = 16 + 30.07 = 46.07 --> d = +- 6.79
t = -4/4 +- 6.79/4 = -1 +- 1.70

a. t = sin 2x = 0.70 --> 2x = 44.43 -->and
2x = 180 - 44.43 = 135.57 deg
2x = 44.43 --> x = 22.22 deg
2x = 135.57 --> x = 67.78 deg
b. t = sin 2x = -2.70 (Rejected)
Check by calculator.
x = 22.22 -> 4sin 2x = 2.80; 2sin^2 2x = 0.98 -> 2.80 + 0.98 = 3.80 OK
x = 67.78; 4sin 2x = 2.80; 2sin^2 2x = 0.98 -> 2.80 + 0.98 = 3.80. OK

Related questions
See all questions in Solving Trigonometric Equations
Impact of this question
1599 views around the world
You can reuse this answer
Creative Commons License