What is the general solution for sin(x)= 6/15 ?

The general solution for sin(x)= 6/15 is x=0.41151…+2pin,x=pi-0.41151…+2pin

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sin(x)= 6/15

sin (x) = \frac{6}{15}

x = 0.41151 \dots + 2 πn, x = π - 0.41151 \dots + 2 πn

Degrees

x = 23.57817 \dots^{\circ} + 36 0^{\circ} n, x = 156.42182 \dots^{\circ} + 36 0^{\circ} n

Solution steps

sin (x) = \frac{6}{15}

Cancel the common factor:

3

sin (x) = \frac{2}{5}

Apply trig inverse properties

sin (x) = \frac{2}{5}

General solutions for

sin (x) = \frac{2}{5}

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

x = arcsin (\frac{2}{5}) + 2 πn, x = π - arcsin (\frac{2}{5}) + 2 πn

x = arcsin (\frac{2}{5}) + 2 πn, x = π - arcsin (\frac{2}{5}) + 2 πn

Show solutions in decimal form

x = 0.41151 \dots + 2 πn, x = π - 0.41151 \dots + 2 πn

What is the general solution for sin(x)= 6/15 ?
The general solution for sin(x)= 6/15 is x=0.41151…+2pin,x=pi-0.41151…+2pin