What is the general solution for tan(2θ)=1.33 ?

The general solution for tan(2θ)=1.33 is θ=(0.92609…)/2+(pin)/2

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tan(2θ)=1.33

tan (2 θ) = 1.33

θ = \frac{0.92609 \dots}{2} + \frac{πn}{2}

Degrees

θ = 26.53061 \dots^{\circ} + 9 0^{\circ} n

Solution steps

tan (2 θ) = 1.33

Apply trig inverse properties

tan (2 θ) = 1.33

General solutions for

tan (2 θ) = 1.33

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

2 θ = arctan (1.33) + πn

2 θ = arctan (1.33) + πn

Solve

2 θ = arctan (1.33) + πn : θ = \frac{arctan ( 1.33 )}{2} + \frac{πn}{2}

2 θ = arctan (1.33) + πn

Divide both sides by

2

2 θ = arctan (1.33) + πn

Divide both sides by

2

\frac{2 θ}{2} = \frac{arctan ( 1.33 )}{2} + \frac{πn}{2}

Simplify

θ = \frac{arctan ( 1.33 )}{2} + \frac{πn}{2}

θ = \frac{arctan ( 1.33 )}{2} + \frac{πn}{2}

θ = \frac{arctan ( 1.33 )}{2} + \frac{πn}{2}

Show solutions in decimal form

θ = \frac{0.92609 \dots}{2} + \frac{πn}{2}

2 cos (2 t) + 2 cos^{2} (t) = 0

5 \cdot cos (x) + 4 - 2 \cdot sin (x) = 0

sin (x) = - 0.54

tan (2 θ) = 1.82

sin (x) = - 0.65

What is the general solution for tan(2θ)=1.33 ?
The general solution for tan(2θ)=1.33 is θ=(0.92609…)/2+(pin)/2