What is the general solution for sin(θ)= 4/5 ,cos(2θ),90<= θ<180 ?

The general solution for sin(θ)= 4/5 ,cos(2θ),90<= θ<180 is No Solution for θ\in\mathbb{R}

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sin(θ)= 4/5 ,cos(2θ),90<= θ<180

sin (θ) = \frac{4}{5}, cos (2 θ), 90 \leq θ < 180

No Solution for θ \in R

Solution steps

sin (θ) = \frac{4}{5}, cos (2 θ), 90 \leq θ < 180

Apply trig inverse properties

sin (θ) = \frac{4}{5}

General solutions for

sin (θ) = \frac{4}{5}

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

θ = arcsin (\frac{4}{5}) + 2 πn, θ = π - arcsin (\frac{4}{5}) + 2 πn

θ = arcsin (\frac{4}{5}) + 2 πn, θ = π - arcsin (\frac{4}{5}) + 2 πn

Solutions for the range

cos (2 θ)

No Solution for θ \in R

What is the general solution for sin(θ)= 4/5 ,cos(2θ),90<= θ<180 ?
The general solution for sin(θ)= 4/5 ,cos(2θ),90<= θ<180 is No Solution for θ\in\mathbb{R}