What is the general solution for sin(x)=(sqrt(2))/4 ?

The general solution for sin(x)=(sqrt(2))/4 is x=0.36136…+2pin,x=pi-0.36136…+2pin

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sin(x)=(sqrt(2))/4

sin (x) = \frac{2}{4}

x = 0.36136 \dots + 2 πn, x = π - 0.36136 \dots + 2 πn

Degrees

x = 20.70481 \dots^{\circ} + 36 0^{\circ} n, x = 159.29518 \dots^{\circ} + 36 0^{\circ} n

Solution steps

sin (x) = \frac{2}{4}

Apply trig inverse properties

sin (x) = \frac{2}{4}

General solutions for

sin (x) = \frac{2}{4}

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

x = arcsin (\frac{2}{4}) + 2 πn, x = π - arcsin (\frac{2}{4}) + 2 πn

x = arcsin (\frac{2}{4}) + 2 πn, x = π - arcsin (\frac{2}{4}) + 2 πn

Show solutions in decimal form

x = 0.36136 \dots + 2 πn, x = π - 0.36136 \dots + 2 πn

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- 5 sin (x) = - 2 cos^{2} (x) + 4, 0 \leq x \leq 2 π

What is the general solution for sin(x)=(sqrt(2))/4 ?
The general solution for sin(x)=(sqrt(2))/4 is x=0.36136…+2pin,x=pi-0.36136…+2pin