What is the general solution for sin(θ)= 5/8 ?

The general solution for sin(θ)= 5/8 is θ=0.67513…+2pin,θ=pi-0.67513…+2pin

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sin(θ)= 5/8

sin (θ) = \frac{5}{8}

θ = 0.67513 \dots + 2 πn, θ = π - 0.67513 \dots + 2 πn

Degrees

θ = 38.68218 \dots^{\circ} + 36 0^{\circ} n, θ = 141.31781 \dots^{\circ} + 36 0^{\circ} n

Solution steps

sin (θ) = \frac{5}{8}

Apply trig inverse properties

sin (θ) = \frac{5}{8}

General solutions for

sin (θ) = \frac{5}{8}

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

θ = arcsin (\frac{5}{8}) + 2 πn, θ = π - arcsin (\frac{5}{8}) + 2 πn

θ = arcsin (\frac{5}{8}) + 2 πn, θ = π - arcsin (\frac{5}{8}) + 2 πn

Show solutions in decimal form

θ = 0.67513 \dots + 2 πn, θ = π - 0.67513 \dots + 2 πn

arctan (2 x) + arctan (x) = \frac{π}{4}

tan (a) = 1

cos (2 θ) = 2, cos^{2} (θ) - 1 = 2, (- \frac{3}{5})^{2} - 1 = - \frac{7}{25}

2 sin (2 θ) = 1, 0 \leq θ \leq 2 π

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

What is the general solution for sin(θ)= 5/8 ?
The general solution for sin(θ)= 5/8 is θ=0.67513…+2pin,θ=pi-0.67513…+2pin