What is the general solution for sin(-θ)=-3/5 ,tan(θ)>0 ?

The general solution for sin(-θ)=-3/5 ,tan(θ)>0 is No Solution for θ\in\mathbb{R}

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sin(-θ)=-3/5 ,tan(θ)>0

sin (- θ) = - \frac{3}{5}, tan (θ) > 0

No Solution for θ \in R

Solution steps

sin (- θ) = - \frac{3}{5}, tan (θ) > 0

Apply trig inverse properties

- θ = arcsin (- \frac{3}{5}) + 2 πn, - θ = π + arcsin (\frac{3}{5}) + 2 πn

Solve

- θ = arcsin (- \frac{3}{5}) + 2 πn : θ = arcsin (\frac{3}{5}) - 2 πn

Solve

- θ = π + arcsin (\frac{3}{5}) + 2 πn : θ = - π - arcsin (\frac{3}{5}) - 2 πn

θ = arcsin (\frac{3}{5}) - 2 πn, θ = - π - arcsin (\frac{3}{5}) - 2 πn

Solutions for the range

tan (θ) > 0

No Solution for θ \in R

tan^{3} (x) + tan^{2} (x) - 3 tan (x) - 3 = 0

tan^{2} (x) + 5 = 3 sec^{2} (x)

tan (x) = \frac{7}{2}

6 cos^{2} (2 x) + 10 cos (4 x) = 12.05718

cos (\frac{θ}{2}) = \frac{1 + \frac{3}{5}}{2}

What is the general solution for sin(-θ)=-3/5 ,tan(θ)>0 ?
The general solution for sin(-θ)=-3/5 ,tan(θ)>0 is No Solution for θ\in\mathbb{R}