What is the general solution for tan(θ)=-2/5 ,sin(θ)>0 ?

The general solution for tan(θ)=-2/5 ,sin(θ)>0 is No Solution for θ\in\mathbb{R}

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tan(θ)=-2/5 ,sin(θ)>0

tan (θ) = - \frac{2}{5}, sin (θ) > 0

No Solution for θ \in R

Solution steps

tan (θ) = - \frac{2}{5}, sin (θ) > 0

Apply trig inverse properties

tan (θ) = - \frac{2}{5}

General solutions for

tan (θ) = - \frac{2}{5}

tan (x) = - a \Rightarrow x = arctan (- a) + πn

θ = arctan (- \frac{2}{5}) + πn

θ = arctan (- \frac{2}{5}) + πn

Solutions for the range

sin (θ) > 0

No Solution for θ \in R

sin (4 θ) = \frac{3}{2}, 0 \leq θ < 2 π

x, z = cot (4 x^{3} y^{6} - 4 x^{4})

sin (θ + \frac{π}{6}) = 2 sin (θ - \frac{π}{6})

4 sin^{2} (x) + 2 cos^{2} (x) - 3 = 0

4 cos^{2} (θ) tan (θ) - tan (θ) = 0

What is the general solution for tan(θ)=-2/5 ,sin(θ)>0 ?
The general solution for tan(θ)=-2/5 ,sin(θ)>0 is No Solution for θ\in\mathbb{R}