What is the general solution for 5sin(X)-2=2sin(X) ?

The general solution for 5sin(X)-2=2sin(X) is X=0.72972…+2pin,X=pi-0.72972…+2pin

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5sin(X)-2=2sin(X)

5 sin (X) - 2 = 2 sin (X)

X = 0.72972 \dots + 2 πn, X = π - 0.72972 \dots + 2 πn

Solution steps

5 sin (X) - 2 = 2 sin (X)

Solve by substitution

sin (X) = \frac{2}{3}

sin (X) = \frac{2}{3} : X = arcsin (\frac{2}{3}) + 2 πn, X = π - arcsin (\frac{2}{3}) + 2 πn

Combine all the solutions

X = arcsin (\frac{2}{3}) + 2 πn, X = π - arcsin (\frac{2}{3}) + 2 πn

Show solutions in decimal form

X = 0.72972 \dots + 2 πn, X = π - 0.72972 \dots + 2 πn

cos^{2} (2 x) + 3 sin (2 x) = 3

- 2 cos^{2} (θ) - 4 sin (θ) + 2 = - 5 sin (θ)

t, x = cos (t) + cos (2 t)

x, sin (x) = - 1

9 - 9 sin (θ) = 6 cos^{2} (θ)

What is the general solution for 5sin(X)-2=2sin(X) ?
The general solution for 5sin(X)-2=2sin(X) is X=0.72972…+2pin,X=pi-0.72972…+2pin