What is the general solution for sin(θ)= 500/680 ?

The general solution for sin(θ)= 500/680 is θ=0.82610…+2pin,θ=pi-0.82610…+2pin

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sin(θ)= 500/680

sin (θ) = \frac{500}{680}

θ = 0.82610 \dots + 2 πn, θ = π - 0.82610 \dots + 2 πn

Degrees

θ = 47.33207 \dots^{\circ} + 36 0^{\circ} n, θ = 132.66792 \dots^{\circ} + 36 0^{\circ} n

Solution steps

sin (θ) = \frac{500}{680}

Cancel the common factor:

20

sin (θ) = \frac{25}{34}

Apply trig inverse properties

sin (θ) = \frac{25}{34}

General solutions for

sin (θ) = \frac{25}{34}

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

θ = arcsin (\frac{25}{34}) + 2 πn, θ = π - arcsin (\frac{25}{34}) + 2 πn

θ = arcsin (\frac{25}{34}) + 2 πn, θ = π - arcsin (\frac{25}{34}) + 2 πn

Show solutions in decimal form

θ = 0.82610 \dots + 2 πn, θ = π - 0.82610 \dots + 2 πn

sin (3 x) + cos (2 x) = 0

cos^{2} (a) - sin^{2} (a) = 2 cos^{2} (a) lo g_{10} (- 1)

tan (x) = - \frac{3}{2}

3 sin (x) cos (x) = sin (x)

cos (\frac{5 x}{10}) = \frac{2}{2}

What is the general solution for sin(θ)= 500/680 ?
The general solution for sin(θ)= 500/680 is θ=0.82610…+2pin,θ=pi-0.82610…+2pin