What is the general solution for sin(θ)=-1/5 ,pi<θ<(3pi)/2 ,cos(θ) ?

The general solution for sin(θ)=-1/5 ,pi<θ<(3pi)/2 ,cos(θ) is θ=pi+0.20135…

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sin(θ)=-1/5 ,pi<θ<(3pi)/2 ,cos(θ)

sin (θ) = - \frac{1}{5}, π < θ < \frac{3 π}{2}, cos (θ)

θ = π + 0.20135 \dots

Degrees

θ = 191.53695 \dots^{\circ}

Solution steps

sin (θ) = - \frac{1}{5}, π < θ < \frac{3 π}{2}, cos (θ)

Apply trig inverse properties

sin (θ) = - \frac{1}{5}

General solutions for

sin (θ) = - \frac{1}{5}

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

θ = arcsin (- \frac{1}{5}) + 2 πn, θ = π + arcsin (\frac{1}{5}) + 2 πn

θ = arcsin (- \frac{1}{5}) + 2 πn, θ = π + arcsin (\frac{1}{5}) + 2 πn

Solutions for the range

π < θ < \frac{3 π}{2}

θ = π + arcsin (\frac{1}{5})

Show solutions in decimal form

θ = π + 0.20135 \dots

3 cot (θ) - 1 = 0, 0 \leq θ \leq 2 π

\frac{sin ( x )}{37} = \frac{sin ( 3 0 ^{\circ} )}{30}

1 - cos (x) = cos (x)

sin^{2} (x) - 1 = 0, 0 \leq x \leq 2 π

2 cos^{3} (θ) = cos (θ)

What is the general solution for sin(θ)=-1/5 ,pi<θ<(3pi)/2 ,cos(θ) ?
The general solution for sin(θ)=-1/5 ,pi<θ<(3pi)/2 ,cos(θ) is θ=pi+0.20135…