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

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

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5sin(θ)=4

5 sin (θ) = 4

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

Degrees

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

Solution steps

5 sin (θ) = 4

Divide both sides by

5

5 sin (θ) = 4

Divide both sides by

5

\frac{5 sin ( θ )}{5} = \frac{4}{5}

Simplify

sin (θ) = \frac{4}{5}

sin (θ) = \frac{4}{5}

Apply trig inverse properties

sin (θ) = \frac{4}{5}

General solutions for

sin (θ) = \frac{4}{5}

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

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

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

Show solutions in decimal form

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

2 cos^{2} (x) - 7 cos (x) = 0

2 cos^{2} (x) - 7 cos (x) = 3

tan (x) = tan (2 x)

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

2 cos^{2} (x) - 1 = 1 - sin^{2} (x)

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