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

The general solution for tan(2θ)=-2/5 is θ=-(0.38050…)/2+(pin)/2

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tan(2θ)=-2/5

tan (2 θ) = - \frac{2}{5}

θ = - \frac{0.38050 \dots}{2} + \frac{πn}{2}

Degrees

θ = - 10.90070 \dots^{\circ} + 9 0^{\circ} n

Solution steps

tan (2 θ) = - \frac{2}{5}

Apply trig inverse properties

tan (2 θ) = - \frac{2}{5}

General solutions for

tan (2 θ) = - \frac{2}{5}

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

2 θ = arctan (- \frac{2}{5}) + πn

2 θ = arctan (- \frac{2}{5}) + πn

Solve

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

2 θ = arctan (- \frac{2}{5}) + πn

Simplify

arctan (- \frac{2}{5}) + πn : - arctan (\frac{2}{5}) + πn

arctan (- \frac{2}{5}) + πn

Use the following property:

arctan (- x) = - arctan (x)

arctan (- \frac{2}{5}) = - arctan (\frac{2}{5})

= - arctan (\frac{2}{5}) + πn

2 θ = - arctan (\frac{2}{5}) + πn

Divide both sides by

2

2 θ = - arctan (\frac{2}{5}) + πn

Divide both sides by

2

\frac{2 θ}{2} = - \frac{arctan ( \frac{2}{5} )}{2} + \frac{πn}{2}

Simplify

θ = - \frac{arctan ( \frac{2}{5} )}{2} + \frac{πn}{2}

θ = - \frac{arctan ( \frac{2}{5} )}{2} + \frac{πn}{2}

θ = - \frac{arctan ( \frac{2}{5} )}{2} + \frac{πn}{2}

Show solutions in decimal form

θ = - \frac{0.38050 \dots}{2} + \frac{πn}{2}

What is the general solution for tan(2θ)=-2/5 ?
The general solution for tan(2θ)=-2/5 is θ=-(0.38050…)/2+(pin)/2