What is the general solution for sin(θ)=(1.5)/2 ?

The general solution for sin(θ)=(1.5)/2 is θ=0.84806…+2pin,θ=pi-0.84806…+2pin

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sin(θ)=(1.5)/2

sin (θ) = \frac{1.5}{2}

θ = 0.84806 \dots + 2 πn, θ = π - 0.84806 \dots + 2 πn

Degrees

θ = 48.59037 \dots^{\circ} + 36 0^{\circ} n, θ = 131.40962 \dots^{\circ} + 36 0^{\circ} n

Solution steps

sin (θ) = \frac{1.5}{2}

Apply trig inverse properties

sin (θ) = \frac{1.5}{2}

General solutions for

sin (θ) = \frac{1.5}{2}

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

θ = arcsin (\frac{1.5}{2}) + 2 πn, θ = π - arcsin (\frac{1.5}{2}) + 2 πn

θ = arcsin (\frac{1.5}{2}) + 2 πn, θ = π - arcsin (\frac{1.5}{2}) + 2 πn

Show solutions in decimal form

θ = 0.84806 \dots + 2 πn, θ = π - 0.84806 \dots + 2 πn

- cos (θ) = cos (θ)

cos (x) = \frac{8}{21}

cos (x) = 0, x = 0

2 cos^{2} (x) - 2 cos (x) - 1 = 0

sin (b) = \frac{1}{3}

What is the general solution for sin(θ)=(1.5)/2 ?
The general solution for sin(θ)=(1.5)/2 is θ=0.84806…+2pin,θ=pi-0.84806…+2pin