Question

How do you find the solutions to `8sin^2(3x) = -7sin(3x)`?

Answer 1

Solve 8sin^2 (3x) = - 7sin (3x)

Ans: `-20^@35 and 80^@35`

Explanation:

`8sin^2 (3x) + 7sin (3x) = 0`
Put sin (3x) in common factor:
`sin (3x)(8sin 3x + 7) = 0`

a. `sin 3x = 0` --> 3x = 0 --> x = 0
`sin 3x = pi` --> `x = pi/3`
`sin 3x = 2pi` --> `x = (2pi)/3`
b. 8sin (3x) + 7 = 0 --> `sin 3x = -7/8`
3x = - 61.04 --> x = `-20^@35`
3x = 180 - (-61.04) = 241.04 --> `x = 80^@35`

Check by calculator
x = 80.35 3x = 241.04 --> sin 3x = -0.875 --> `sin^2 (3x) = 0.77`
`8sin^2 (3x) = 0.77(8) = 6.12` --> `-7sin 3x = 7(0.875) = 6.125`. OK