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}

Solution steps

tan (2 θ) = - \frac{2}{5}

Apply trig inverse properties

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}

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

Show solutions in decimal form

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

cos (2 x) - 3 cos (x) = - 2

3 cos (x) - 3 sin (x) = 0

cos^{2} (3 x) = cos (9 x^{2})

2 cos (θ) - 2 = 0

x, y = r (sec (x))

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