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

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

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3sin(x)-2=0

3 sin (x) - 2 = 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

3 sin (x) - 2 = 0

Move

2

to the right side

3 sin (x) - 2 = 0

Add

2

to both sides

3 sin (x) - 2 + 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

4 cos^{2} (x) - 2 sin (x) + 1 = 0

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

tan (x) + 1 = - \frac{1}{3} - \frac{1}{3} cot (x)

6 cos^{2} (x) + 7 cos (x) + 2 = 0

sin (θ) = \frac{4}{5}, 0 < θ < \frac{π}{2}, sin (2 θ)

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