What is the general solution for sin(θ)=-4/5 ,(7pi)/2 <= θ<4pi,cos(2θ) ?

The general solution for sin(θ)=-4/5 ,(7pi)/2 <= θ<4pi,cos(2θ) is θ=-0.92729…+4pi

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sin(θ)=-4/5 ,(7pi)/2 <= θ<4pi,cos(2θ)

sin (θ) = - \frac{4}{5}, \frac{7 π}{2} \leq θ < 4 π, cos (2 θ)

θ = - 0.92729 \dots + 4 π

Solution steps

sin (θ) = - \frac{4}{5}, \frac{7 π}{2} \leq θ < 4 π, cos (2 θ)

Apply trig inverse properties

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

Solutions for the range

\frac{7 π}{2} \leq θ < 4 π

θ = - arcsin (\frac{4}{5}) + 4 π

Show solutions in decimal form

θ = - 0.92729 \dots + 4 π

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

- 8 sin (θ) = - 3

sin (x) + 1 = 1

- 12 cot (x) - 43 = 0

3 sin^{2} (t) = 2 cos (t) sin (t)

What is the general solution for sin(θ)=-4/5 ,(7pi)/2 <= θ<4pi,cos(2θ) ?
The general solution for sin(θ)=-4/5 ,(7pi)/2 <= θ<4pi,cos(2θ) is θ=-0.92729…+4pi