What is the general solution for tan(2θ)=0.5 ?

The general solution for tan(2θ)=0.5 is θ=(0.46364…)/2+(pin)/2

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tan(2θ)=0.5

tan (2 θ) = 0.5

θ = \frac{0.46364 \dots}{2} + \frac{πn}{2}

Degrees

θ = 13.28252 \dots^{\circ} + 9 0^{\circ} n

Solution steps

tan (2 θ) = 0.5

Apply trig inverse properties

tan (2 θ) = 0.5

General solutions for

tan (2 θ) = 0.5

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

2 θ = arctan (0.5) + πn

2 θ = arctan (0.5) + πn

Solve

2 θ = arctan (0.5) + πn : θ = \frac{arctan ( 0.5 )}{2} + \frac{πn}{2}

2 θ = arctan (0.5) + πn

Divide both sides by

2

2 θ = arctan (0.5) + πn

Divide both sides by

2

\frac{2 θ}{2} = \frac{arctan ( 0.5 )}{2} + \frac{πn}{2}

Simplify

θ = \frac{arctan ( 0.5 )}{2} + \frac{πn}{2}

θ = \frac{arctan ( 0.5 )}{2} + \frac{πn}{2}

θ = \frac{arctan ( 0.5 )}{2} + \frac{πn}{2}

Show solutions in decimal form

θ = \frac{0.46364 \dots}{2} + \frac{πn}{2}

146 = (8 - cos (θ))^{2} + (- 9 - sin (θ))^{2}

cos (x) = \frac{9}{10}

34 \cdot sin (\frac{π}{6} (x - 4.3)) = 34

2 (sin (x)) 2 - 5 cos (x) - 4 = 0

cos (\frac{x}{2} + 2 0^{\circ}) = sin (x)

What is the general solution for tan(2θ)=0.5 ?
The general solution for tan(2θ)=0.5 is θ=(0.46364…)/2+(pin)/2