What is the general solution for sin(θ)= 3/8 , pi/2 <θ<pi ?

The general solution for sin(θ)= 3/8 , pi/2 <θ<pi is θ=pi-0.38439…

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sin(θ)= 3/8 , pi/2 <θ<pi

sin (θ) = \frac{3}{8}, \frac{π}{2} < θ < π

θ = π - 0.38439 \dots

Degrees

θ = 157.97568 \dots^{\circ}

Solution steps

sin (θ) = \frac{3}{8}, \frac{π}{2} < θ < π

Apply trig inverse properties

sin (θ) = \frac{3}{8}

General solutions for

sin (θ) = \frac{3}{8}

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

θ = arcsin (\frac{3}{8}) + 2 πn, θ = π - arcsin (\frac{3}{8}) + 2 πn

θ = arcsin (\frac{3}{8}) + 2 πn, θ = π - arcsin (\frac{3}{8}) + 2 πn

Solutions for the range

\frac{π}{2} < θ < π

θ = π - arcsin (\frac{3}{8})

Show solutions in decimal form

θ = π - 0.38439 \dots

3 cos (x) = 5 sin (x)

4 cos (x) = 3 sin (x)

cos (π x) = 0, 0 \leq x \leq 2 π

cos (2 x - 1 5^{\circ}) = - sin (6 0^{\circ} - 3 x)

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

What is the general solution for sin(θ)= 3/8 , pi/2 <θ<pi ?
The general solution for sin(θ)= 3/8 , pi/2 <θ<pi is θ=pi-0.38439…