What is the general solution for tan(2θ)=1.333 ?

The general solution for tan(2θ)=1.333 is θ=(0.92717…)/2+(pin)/2

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tan(2θ)=1.333

tan (2 θ) = 1.333

θ = \frac{0.92717 \dots}{2} + \frac{πn}{2}

Degrees

θ = 26.56161 \dots^{\circ} + 9 0^{\circ} n

Solution steps

tan (2 θ) = 1.333

Apply trig inverse properties

tan (2 θ) = 1.333

General solutions for

tan (2 θ) = 1.333

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

2 θ = arctan (1.333) + πn

2 θ = arctan (1.333) + πn

Solve

2 θ = arctan (1.333) + πn : θ = \frac{arctan ( 1.333 )}{2} + \frac{πn}{2}

2 θ = arctan (1.333) + πn

Divide both sides by

2

2 θ = arctan (1.333) + πn

Divide both sides by

2

\frac{2 θ}{2} = \frac{arctan ( 1.333 )}{2} + \frac{πn}{2}

Simplify

θ = \frac{arctan ( 1.333 )}{2} + \frac{πn}{2}

θ = \frac{arctan ( 1.333 )}{2} + \frac{πn}{2}

θ = \frac{arctan ( 1.333 )}{2} + \frac{πn}{2}

Show solutions in decimal form

θ = \frac{0.92717 \dots}{2} + \frac{πn}{2}

What is the general solution for tan(2θ)=1.333 ?
The general solution for tan(2θ)=1.333 is θ=(0.92717…)/2+(pin)/2