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

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

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solvefor θ,2sin(θ)=1.5

solve for

θ, 2 sin (θ) = 1.5

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

2 sin (θ) = 1.5

Divide both sides by

2

2 sin (θ) = 1.5

Divide both sides by

2

\frac{2 sin ( θ )}{2} = \frac{1.5}{2}

Simplify

sin (θ) = 0.75

sin (θ) = 0.75

Apply trig inverse properties

sin (θ) = 0.75

General solutions for

sin (θ) = 0.75

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

θ = arcsin (0.75) + 2 πn, θ = π - arcsin (0.75) + 2 πn

θ = arcsin (0.75) + 2 πn, θ = π - arcsin (0.75) + 2 πn

Show solutions in decimal form

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

cos (θ) = - 2109

x, cos (x) (cos (x) - sin (x)) = 0

sin (x) = 0.72555

15 = 10 sin (\frac{π}{20} (x + 10)) + 12

- cos (x) = \frac{2}{20}

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