What is the general solution for sin(216)=sin(θ) ?

The general solution for sin(216)=sin(θ) is θ=-0.62831…+360n,θ=180+0.62831…+360n

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sin(216)=sin(θ)

sin (21 6^{\circ}) = sin (θ)

θ = - 0.62831 \dots + 36 0^{\circ} n, θ = 18 0^{\circ} + 0.62831 \dots + 36 0^{\circ} n

Solution steps

sin (21 6^{\circ}) = sin (θ)

sin (21 6^{\circ}) = - \frac{2 5 - 5}{4}

- \frac{2 5 - 5}{4} = sin (θ)

Switch sides

sin (θ) = - \frac{2 5 - 5}{4}

Apply trig inverse properties

θ = arcsin (- \frac{2 5 - 5}{4}) + 36 0^{\circ} n, θ = 18 0^{\circ} + arcsin (\frac{2 5 - 5}{4}) + 36 0^{\circ} n

Show solutions in decimal form

θ = - 0.62831 \dots + 36 0^{\circ} n, θ = 18 0^{\circ} + 0.62831 \dots + 36 0^{\circ} n

cos (θ) = - 0.2

sin^{2} (x) - 5 cos (x) = 3

cos (x) = - \frac{9}{41}

5 sin (y) = 3 sin (y) + 3

2 sin^{2} (θ) + sin^{2} (θ) = 0

What is the general solution for sin(216)=sin(θ) ?
The general solution for sin(216)=sin(θ) is θ=-0.62831…+360n,θ=180+0.62831…+360n