What is the general solution for sin(x)=(1.2)/(sqrt(10)) ?

The general solution for sin(x)=(1.2)/(sqrt(10)) is x=0.38922…+2pin,x=pi-0.38922…+2pin

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sin(x)=(1.2)/(sqrt(10))

sin (x) = \frac{1.2}{10}

x = 0.38922 \dots + 2 πn, x = π - 0.38922 \dots + 2 πn

Solution steps

sin (x) = \frac{1.2}{10}

Simplify

\frac{1.2}{10} : \frac{10 \cdot 1.2}{10}

Apply trig inverse properties

x = arcsin (\frac{10 \cdot 1.2}{10}) + 2 πn, x = π - arcsin (\frac{10 \cdot 1.2}{10}) + 2 πn

Show solutions in decimal form

x = 0.38922 \dots + 2 πn, x = π - 0.38922 \dots + 2 πn

t, x = - 3 cos (π t)

\frac{- 1}{2} = cos (x)

cos (2 t) - sin (t) = 0.5, 0 \leq t \leq 2 π

sin (2 x) = 0.1

sin (\frac{π}{2} - x) tan (x) = cos (x)

What is the general solution for sin(x)=(1.2)/(sqrt(10)) ?
The general solution for sin(x)=(1.2)/(sqrt(10)) is x=0.38922…+2pin,x=pi-0.38922…+2pin