What is the general solution for tan(2θ)=1.82 ?

The general solution for tan(2θ)=1.82 is θ=(1.06837…)/2+(pin)/2

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tan(2θ)=1.82

tan (2 θ) = 1.82

θ = \frac{1.06837 \dots}{2} + \frac{πn}{2}

Degrees

θ = 30.60669 \dots^{\circ} + 9 0^{\circ} n

Solution steps

tan (2 θ) = 1.82

Apply trig inverse properties

tan (2 θ) = 1.82

General solutions for

tan (2 θ) = 1.82

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

2 θ = arctan (1.82) + πn

2 θ = arctan (1.82) + πn

Solve

2 θ = arctan (1.82) + πn : θ = \frac{arctan ( 1.82 )}{2} + \frac{πn}{2}

2 θ = arctan (1.82) + πn

Divide both sides by

2

2 θ = arctan (1.82) + πn

Divide both sides by

2

\frac{2 θ}{2} = \frac{arctan ( 1.82 )}{2} + \frac{πn}{2}

Simplify

θ = \frac{arctan ( 1.82 )}{2} + \frac{πn}{2}

θ = \frac{arctan ( 1.82 )}{2} + \frac{πn}{2}

θ = \frac{arctan ( 1.82 )}{2} + \frac{πn}{2}

Show solutions in decimal form

θ = \frac{1.06837 \dots}{2} + \frac{πn}{2}

sin (x) = - 0.65

sin (x) = - 0.71

cos (x) tan (x) - tan (x) = 0

sin (x) = - 0.98

2 cos^{2} (x) + 9 cos (x) = 4

What is the general solution for tan(2θ)=1.82 ?
The general solution for tan(2θ)=1.82 is θ=(1.06837…)/2+(pin)/2