What is the general solution for tan(2θ)=0.55 ?

The general solution for tan(2θ)=0.55 is θ=(0.50284…)/2+(pin)/2

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tan(2θ)=0.55

tan (2 θ) = 0.55

θ = \frac{0.50284 \dots}{2} + \frac{πn}{2}

Degrees

θ = 14.40539 \dots^{\circ} + 9 0^{\circ} n

Solution steps

tan (2 θ) = 0.55

Apply trig inverse properties

tan (2 θ) = 0.55

General solutions for

tan (2 θ) = 0.55

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

2 θ = arctan (0.55) + πn

2 θ = arctan (0.55) + πn

Solve

2 θ = arctan (0.55) + πn : θ = \frac{arctan ( 0.55 )}{2} + \frac{πn}{2}

2 θ = arctan (0.55) + πn

Divide both sides by

2

2 θ = arctan (0.55) + πn

Divide both sides by

2

\frac{2 θ}{2} = \frac{arctan ( 0.55 )}{2} + \frac{πn}{2}

Simplify

θ = \frac{arctan ( 0.55 )}{2} + \frac{πn}{2}

θ = \frac{arctan ( 0.55 )}{2} + \frac{πn}{2}

θ = \frac{arctan ( 0.55 )}{2} + \frac{πn}{2}

Show solutions in decimal form

θ = \frac{0.50284 \dots}{2} + \frac{πn}{2}

What is the general solution for tan(2θ)=0.55 ?
The general solution for tan(2θ)=0.55 is θ=(0.50284…)/2+(pin)/2