What is the general solution for 8sin(120-x)=9sin(x) ?

The general solution for 8sin(120-x)=9sin(x) is x=0.94566…+180n

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8sin(120-x)=9sin(x)

8 sin (12 0^{\circ} - x) = 9 sin (x)

x = 0.94566 \dots + 18 0^{\circ} n

Solution steps

8 sin (12 0^{\circ} - x) = 9 sin (x)

Rewrite using trig identities

8 (\frac{3}{2} cos (x) + \frac{1}{2} sin (x)) = 9 sin (x)

Subtract

9 sin (x)

from both sides

43 cos (x) - 5 sin (x) = 0

Rewrite using trig identities

43 - 5 tan (x) = 0

Move

43

to the right side

- 5 tan (x) = - 43

Divide both sides by

- 5

tan (x) = \frac{4 3}{5}

Apply trig inverse properties

x = arctan (\frac{4 3}{5}) + 18 0^{\circ} n

Show solutions in decimal form

x = 0.94566 \dots + 18 0^{\circ} n

cos (θ) = 0.625

x, sin (x) = 3 cos (x)

x, 1.12 = 0.04 sin (x)

sin (2 x) = - 0.8

cos (2 x - \frac{π}{5}) = 0

What is the general solution for 8sin(120-x)=9sin(x) ?
The general solution for 8sin(120-x)=9sin(x) is x=0.94566…+180n