What is the general solution for sin(θ)=-4/7 ,pi<θ<(3pi)/2 ,cos(2θ) ?

The general solution for sin(θ)=-4/7 ,pi<θ<(3pi)/2 ,cos(2θ) is θ=pi+0.60824…

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sin(θ)=-4/7 ,pi<θ<(3pi)/2 ,cos(2θ)

sin (θ) = - \frac{4}{7}, π < θ < \frac{3 π}{2}, cos (2 θ)

θ = π + 0.60824 \dots

Solution steps

sin (θ) = - \frac{4}{7}, π < θ < \frac{3 π}{2}, cos (2 θ)

Apply trig inverse properties

θ = arcsin (- \frac{4}{7}) + 2 πn, θ = π + arcsin (\frac{4}{7}) + 2 πn

Solutions for the range

π < θ < \frac{3 π}{2}

θ = π + arcsin (\frac{4}{7})

Show solutions in decimal form

θ = π + 0.60824 \dots

tan (θ) = - \frac{2}{5}

(tan (x) - 1) (3 tan (x) + 1) = 0

sec (2 x) + 1 = 0

sin (θ) = - \frac{4}{7}

6 cos (6 x) = 5

What is the general solution for sin(θ)=-4/7 ,pi<θ<(3pi)/2 ,cos(2θ) ?
The general solution for sin(θ)=-4/7 ,pi<θ<(3pi)/2 ,cos(2θ) is θ=pi+0.60824…