What is the general solution for cos(θ)=-4/5 ,sin(2θ),180<θ<270 ?

The general solution for cos(θ)=-4/5 ,sin(2θ),180<θ<270 is No Solution for θ\in\mathbb{R}

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cos(θ)=-4/5 ,sin(2θ),180<θ<270

cos (θ) = - \frac{4}{5}, sin (2 θ), 18 0^{\circ} < θ < 27 0^{\circ}

No Solution for θ \in R

Solution steps

cos (θ) = - \frac{4}{5}, sin (2 θ), 18 0^{\circ} < θ < 27 0^{\circ}

Apply trig inverse properties

cos (θ) = - \frac{4}{5}

General solutions for

cos (θ) = - \frac{4}{5}

cos (x) = - a \Rightarrow x = arccos (- a) + 2 πn, x = - arccos (- a) + 2 πn

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

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

Solutions for the range

sin (2 θ)

No Solution for θ \in R

What is the general solution for cos(θ)=-4/5 ,sin(2θ),180<θ<270 ?
The general solution for cos(θ)=-4/5 ,sin(2θ),180<θ<270 is No Solution for θ\in\mathbb{R}