Approximate the solutions (to three decimal places) of the given equation in

Question

the interval

(- pi/2, pi/2)

6 sin 2x − 8 cos x + 9 sin x = 6

Can you help with this please? I am studying for my Pre Calculus 1 exam and am stuck on this question...!

The answer options are
a. x = 0.398
b. x = 0.094
c. x = 0.139
d. x = 0.730
e. x = 1.336

Answer 1

6 sin 2x − 8 cos x + 9 sin x = 6
12sinxcosx - 8cosx + 9sinx - 6 = 0
4cosx(3sinx - 2) + 3(3sinx - 2) = 0
(3sinx - 2)(4cosx + 3) = 0
sinx = 2/3 OR cosx = -3/4, the last one is not possible

sinx = 2/3
x = .7297..
which matches b)

Make sure your calculator is set to radians for these type of questions, unless the question specifies degrees.