Question

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

Answer 1

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