What is the general solution for sin(θ)= 12/20 ?

The general solution for sin(θ)= 12/20 is θ=0.64350…+2pin,θ=pi-0.64350…+2pin

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sin(θ)= 12/20

sin (θ) = \frac{12}{20}

θ = 0.64350 \dots + 2 πn, θ = π - 0.64350 \dots + 2 πn

Degrees

θ = 36.86989 \dots^{\circ} + 36 0^{\circ} n, θ = 143.13010 \dots^{\circ} + 36 0^{\circ} n

Solution steps

sin (θ) = \frac{12}{20}

Cancel the common factor:

4

sin (θ) = \frac{3}{5}

Apply trig inverse properties

sin (θ) = \frac{3}{5}

General solutions for

sin (θ) = \frac{3}{5}

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

θ = arcsin (\frac{3}{5}) + 2 πn, θ = π - arcsin (\frac{3}{5}) + 2 πn

θ = arcsin (\frac{3}{5}) + 2 πn, θ = π - arcsin (\frac{3}{5}) + 2 πn

Show solutions in decimal form

θ = 0.64350 \dots + 2 πn, θ = π - 0.64350 \dots + 2 πn

cos (x) = 0.914

8 + 2 cot (x) = 12, 0^{\circ} < x < 9 0^{\circ}

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

2 sin^{3} (x) + 1 = 0

cos (2 x + \frac{π}{6}) = \frac{1}{2}

What is the general solution for sin(θ)= 12/20 ?
The general solution for sin(θ)= 12/20 is θ=0.64350…+2pin,θ=pi-0.64350…+2pin