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

The general solution for sin(θ)= 2/3 , pi/2 <θ<pi,cos(2θ)=x is θ=pi-0.72972…

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sin(θ)= 2/3 , pi/2 <θ<pi,cos(2θ)=x

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

θ = π - 0.72972 \dots

Degrees

θ = 138.18968 \dots^{\circ}

Solution steps

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

Apply trig inverse properties

sin (θ) = \frac{2}{3}

General solutions for

sin (θ) = \frac{2}{3}

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

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

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

Solutions for the range

\frac{π}{2} < θ < π

θ = π - arcsin (\frac{2}{3})

Show solutions in decimal form

θ = π - 0.72972 \dots

tan (3 x) = 2

tan (θ) = 3 - π

sin (x) = \frac{15}{39}

tan (a) = \frac{40}{12.5}

csc (θ) = 1.3127

What is the general solution for sin(θ)= 2/3 , pi/2 <θ<pi,cos(2θ)=x ?
The general solution for sin(θ)= 2/3 , pi/2 <θ<pi,cos(2θ)=x is θ=pi-0.72972…