What is the general solution for sin(θ)=0.15 ?

The general solution for sin(θ)=0.15 is θ=0.15056…+2pin,θ=pi-0.15056…+2pin

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sin(θ)=0.15

sin (θ) = 0.15

θ = 0.15056 \dots + 2 πn, θ = π - 0.15056 \dots + 2 πn

Degrees

θ = 8.62692 \dots^{\circ} + 36 0^{\circ} n, θ = 171.37307 \dots^{\circ} + 36 0^{\circ} n

Solution steps

sin (θ) = 0.15

Apply trig inverse properties

sin (θ) = 0.15

General solutions for

sin (θ) = 0.15

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

θ = arcsin (0.15) + 2 πn, θ = π - arcsin (0.15) + 2 πn

θ = arcsin (0.15) + 2 πn, θ = π - arcsin (0.15) + 2 πn

Show solutions in decimal form

θ = 0.15056 \dots + 2 πn, θ = π - 0.15056 \dots + 2 πn

6 cos (2 θ) = 6 cos (θ)

tan (\frac{θ}{2}) = csc^{2} (θ) - cot^{2} (θ)

6 cos^{2} (x) - sin (x) - 4 = 0

cot^{2} (x) = \frac{3}{2} csc (x)

2 cos (θ) - 1 = 0, 0 \leq θ \leq 2 π

What is the general solution for sin(θ)=0.15 ?
The general solution for sin(θ)=0.15 is θ=0.15056…+2pin,θ=pi-0.15056…+2pin