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

Solution steps

2 - 3 sin (x) = 0

Move

2

to the right side

- 3 sin (x) = - 2

Divide both sides by

- 3

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

Apply trig inverse properties

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