What is the general solution for 2-3sin(x)=0 ?

The general solution for 2-3sin(x)=0 is x=0.72972…+2pin,x=pi-0.72972…+2pin

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2-3sin(x)=0

2 - 3 sin (x) = 0

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

Degrees

x = 41.81031 \dots^{\circ} + 36 0^{\circ} n, x = 138.18968 \dots^{\circ} + 36 0^{\circ} n

Solution steps

2 - 3 sin (x) = 0

Move

2

to the right side

2 - 3 sin (x) = 0

Subtract

2

from both sides

2 - 3 sin (x) - 2 = 0 - 2

Simplify

- 3 sin (x) = - 2

- 3 sin (x) = - 2

Divide both sides by

- 3

- 3 sin (x) = - 2

Divide both sides by

- 3

\frac{- 3 sin ( x )}{- 3} = \frac{- 2}{- 3}

Simplify

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

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

Apply trig inverse properties

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

General solutions for

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

sin (x) = a \Rightarrow x = arcsin (a) + 2 πn, x = π - arcsin (a) + 2 πn

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

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

y = cos (x), x

\frac{cos ( θ )}{sin ( θ )} = 0

sin (2 x) = sin (x), 0 \leq x < 2 π

tan (θ) = \frac{5}{5 3}

7 cos (x) = 2 + 5 cos (x)

What is the general solution for 2-3sin(x)=0 ?
The general solution for 2-3sin(x)=0 is x=0.72972…+2pin,x=pi-0.72972…+2pin