What is the general solution for 9sin(x)-2=4sin^2(x) ?

The general solution for 9sin(x)-2=4sin^2(x) is x=0.25268…+2pin,x=pi-0.25268…+2pin

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9sin(x)-2=4sin^2(x)

9 sin (x) - 2 = 4 sin^{2} (x)

x = 0.25268 \dots + 2 πn, x = π - 0.25268 \dots + 2 πn

Solution steps

9 sin (x) - 2 = 4 sin^{2} (x)

Solve by substitution

sin (x) = 2, sin (x) = \frac{1}{4}

sin (x) = 2 :

No Solution

sin (x) = \frac{1}{4} : x = arcsin (\frac{1}{4}) + 2 πn, x = π - arcsin (\frac{1}{4}) + 2 πn

Combine all the solutions

x = arcsin (\frac{1}{4}) + 2 πn, x = π - arcsin (\frac{1}{4}) + 2 πn

Show solutions in decimal form

x = 0.25268 \dots + 2 πn, x = π - 0.25268 \dots + 2 πn

- a c_{1} sin (a x) + a c_{2} cos (a x) = 0

3 - 3 cos (x) = 0

- 2 cot (x) = csc^{2} (x)

sin (θ) = - 0.671

cos (y) = sin (y)

What is the general solution for 9sin(x)-2=4sin^2(x) ?
The general solution for 9sin(x)-2=4sin^2(x) is x=0.25268…+2pin,x=pi-0.25268…+2pin