Question

Trig question

Answer 1

5 cos x - 12 sin x = -3
find x

I'll post my working... please let me finish first

Answer 2

So far I have:

-12 sin x + 5 cos x = -3
13 sin (x - 22.62) = -3
sin (x - 22.62) = -3/13
x - 22.62 = -13.34
x = 9.28 and 170.72

These don't work though

Answer 3

I think when you arc sin both sides you had your calculator in degree mode instead of radians.

Answer 4

@Romero, sorry I forgot to put 0° ≤ x ≤ 360°

Answer 5

\[5 \cos x - 12 \sin x = -3\]\[5 \cos x = 12 \sin x - 3\]square both sides\[25 \ \cos^{2} x = 144 \ \sin^{2} x - 72 \sin x + 9\]\[25(1 - \sin^2 x) = 144 \ \sin^2 x - 72 \sin x + 9\]\[169 \ \sin^2 x - 72 \sin x - 16 = 0\]use the quadratic formula to solve for sin x

Answer 6

Your answer should involve either Arccos or ArcSin.