What is the general solution for 4sin(θ)=1 ?

The general solution for 4sin(θ)=1 is θ=0.25268…+2pin,θ=pi-0.25268…+2pin

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4sin(θ)=1

4 sin (θ) = 1

θ = 0.25268 \dots + 2 πn, θ = π - 0.25268 \dots + 2 πn

Degrees

θ = 14.47751 \dots^{\circ} + 36 0^{\circ} n, θ = 165.52248 \dots^{\circ} + 36 0^{\circ} n

Solution steps

4 sin (θ) = 1

Divide both sides by

4

4 sin (θ) = 1

Divide both sides by

4

\frac{4 sin ( θ )}{4} = \frac{1}{4}

Simplify

sin (θ) = \frac{1}{4}

sin (θ) = \frac{1}{4}

Apply trig inverse properties

sin (θ) = \frac{1}{4}

General solutions for

sin (θ) = \frac{1}{4}

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

θ = arcsin (\frac{1}{4}) + 2 πn, θ = π - arcsin (\frac{1}{4}) + 2 πn

θ = arcsin (\frac{1}{4}) + 2 πn, θ = π - arcsin (\frac{1}{4}) + 2 πn

Show solutions in decimal form

θ = 0.25268 \dots + 2 πn, θ = π - 0.25268 \dots + 2 πn

sin (x + \frac{π}{2}) = 0.6

4 cot (x) + 1 = 1 + 2 cot (x)

\frac{2}{3} = sin (θ) - 0.28 cos (θ)

2 sin (x) = 3 - cos (x), 0 \leq x \leq 2 π

cos^{2} (x) = - \frac{1}{3}

What is the general solution for 4sin(θ)=1 ?
The general solution for 4sin(θ)=1 is θ=0.25268…+2pin,θ=pi-0.25268…+2pin