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

The general solution for sin(θ)=-(sqrt(5))/5 ,(3pi)/2 <θ<2pi is θ=-0.46364…+2pi

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sin(θ)=-(sqrt(5))/5 ,(3pi)/2 <θ<2pi

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

θ = - 0.46364 \dots + 2 π

Degrees

θ = 333.43494 \dots^{\circ}

Solution steps

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

Apply trig inverse properties

sin (θ) = - \frac{5}{5}

General solutions for

sin (θ) = - \frac{5}{5}

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

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

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

Solutions for the range

\frac{3 π}{2} < θ < 2 π

θ = - arcsin (\frac{5}{5}) + 2 π

Show solutions in decimal form

θ = - 0.46364 \dots + 2 π

(2 sin (2 x) - 1) (3 tan (2 x) - 1) = 0

- 0.2588 + 0.9659 tan (b) = 1.4201

2 cot^{2} (t) sin (t) - cot^{2} (t) = 0

7 cos (x) = - 1

2 sin^{2} (θ) + cos (θ) - 2 = - 1

What is the general solution for sin(θ)=-(sqrt(5))/5 ,(3pi)/2 <θ<2pi ?
The general solution for sin(θ)=-(sqrt(5))/5 ,(3pi)/2 <θ<2pi is θ=-0.46364…+2pi