What is the general solution for sin(θ)= 2/7 ?

The general solution for sin(θ)= 2/7 is θ=0.28975…+2pin,θ=pi-0.28975…+2pin

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sin(θ)= 2/7

sin (θ) = \frac{2}{7}

θ = 0.28975 \dots + 2 πn, θ = π - 0.28975 \dots + 2 πn

Degrees

θ = 16.60154 \dots^{\circ} + 36 0^{\circ} n, θ = 163.39845 \dots^{\circ} + 36 0^{\circ} n

Solution steps

sin (θ) = \frac{2}{7}

Apply trig inverse properties

sin (θ) = \frac{2}{7}

General solutions for

sin (θ) = \frac{2}{7}

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

θ = arcsin (\frac{2}{7}) + 2 πn, θ = π - arcsin (\frac{2}{7}) + 2 πn

θ = arcsin (\frac{2}{7}) + 2 πn, θ = π - arcsin (\frac{2}{7}) + 2 πn

Show solutions in decimal form

θ = 0.28975 \dots + 2 πn, θ = π - 0.28975 \dots + 2 πn

2 sec (x) - 5 = 0

tan (a) + cot (a) = sec (a) cos (a)

- 5 tan^{2} (θ) + 3 = 8 tan (θ) + 6

cos (θ) = \frac{- 3}{13}

cos (x) = 0.84

What is the general solution for sin(θ)= 2/7 ?
The general solution for sin(θ)= 2/7 is θ=0.28975…+2pin,θ=pi-0.28975…+2pin