What is the general solution for sin(θ)= 563/2000 ?

The general solution for sin(θ)= 563/2000 is θ=0.28535…+2pin,θ=pi-0.28535…+2pin

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sin(θ)= 563/2000

sin (θ) = \frac{563}{2000}

θ = 0.28535 \dots + 2 πn, θ = π - 0.28535 \dots + 2 πn

Degrees

θ = 16.34974 \dots^{\circ} + 36 0^{\circ} n, θ = 163.65025 \dots^{\circ} + 36 0^{\circ} n

Solution steps

sin (θ) = \frac{563}{2000}

Apply trig inverse properties

sin (θ) = \frac{563}{2000}

General solutions for

sin (θ) = \frac{563}{2000}

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

θ = arcsin (\frac{563}{2000}) + 2 πn, θ = π - arcsin (\frac{563}{2000}) + 2 πn

θ = arcsin (\frac{563}{2000}) + 2 πn, θ = π - arcsin (\frac{563}{2000}) + 2 πn

Show solutions in decimal form

θ = 0.28535 \dots + 2 πn, θ = π - 0.28535 \dots + 2 πn

6 sec (2 x) - 8 = 0

0 = cos (x) + cos (2 x)

8 cos^{2} (x) = 2

arctan (t) + 1 = 1

2 cos^{2} (θ) - 7 cos (θ) + 3 = 0, 0 < θ < 2 π

What is the general solution for sin(θ)= 563/2000 ?
The general solution for sin(θ)= 563/2000 is θ=0.28535…+2pin,θ=pi-0.28535…+2pin