What is the general solution for sin(x)= 4/5 ?

The general solution for sin(x)= 4/5 is x=0.92729…+2pin,x=pi-0.92729…+2pin

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sin(x)= 4/5

sin (x) = \frac{4}{5}

x = 0.92729 \dots + 2 πn, x = π - 0.92729 \dots + 2 πn

Degrees

x = 53.13010 \dots^{\circ} + 36 0^{\circ} n, x = 126.86989 \dots^{\circ} + 36 0^{\circ} n

Solution steps

sin (x) = \frac{4}{5}

Apply trig inverse properties

sin (x) = \frac{4}{5}

General solutions for

sin (x) = \frac{4}{5}

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

x = arcsin (\frac{4}{5}) + 2 πn, x = π - arcsin (\frac{4}{5}) + 2 πn

x = arcsin (\frac{4}{5}) + 2 πn, x = π - arcsin (\frac{4}{5}) + 2 πn

Show solutions in decimal form

x = 0.92729 \dots + 2 πn, x = π - 0.92729 \dots + 2 πn

4 sin^{2} (θ) = 3 cos^{2} (θ), 0^{\circ} < θ < 36 0^{\circ}

2 sin (x) - 2 = 0

tan (θ) = \frac{1}{2}

sin^{2} (x) + cos (x) + 1 = 0

2 cos (2 x) = 0

What is the general solution for sin(x)= 4/5 ?
The general solution for sin(x)= 4/5 is x=0.92729…+2pin,x=pi-0.92729…+2pin