What is the general solution for sin(x)= 4/6 ?

The general solution for sin(x)= 4/6 is x=0.72972…+2pin,x=pi-0.72972…+2pin

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sin(x)= 4/6

sin (x) = \frac{4}{6}

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

Solution steps

sin (x) = \frac{4}{6}

Cancel the common factor:

2

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

- 4 sin (x) = 0

4 sin^{2} (θ) - sin (θ) - 4 = 0

tan (θ) = 1

sin (2 θ) + cos (2 θ) = 0

5 cot^{2} (x) - 15 = 0

What is the general solution for sin(x)= 4/6 ?
The general solution for sin(x)= 4/6 is x=0.72972…+2pin,x=pi-0.72972…+2pin