What is the general solution for tan(a/2)= 1/2 ?

The general solution for tan(a/2)= 1/2 is a=2*0.46364…+2pin

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tan(a/2)= 1/2

tan (\frac{a}{2}) = \frac{1}{2}

a = 2 \cdot 0.46364 \dots + 2 πn

Degrees

a = 53.13010 \dots^{\circ} + 36 0^{\circ} n

Solution steps

tan (\frac{a}{2}) = \frac{1}{2}

Apply trig inverse properties

tan (\frac{a}{2}) = \frac{1}{2}

General solutions for

tan (\frac{a}{2}) = \frac{1}{2}

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

\frac{a}{2} = arctan (\frac{1}{2}) + πn

\frac{a}{2} = arctan (\frac{1}{2}) + πn

Solve

\frac{a}{2} = arctan (\frac{1}{2}) + πn : a = 2 arctan (\frac{1}{2}) + 2 πn

\frac{a}{2} = arctan (\frac{1}{2}) + πn

Multiply both sides by

2

\frac{a}{2} = arctan (\frac{1}{2}) + πn

Multiply both sides by

2

\frac{2 a}{2} = 2 arctan (\frac{1}{2}) + 2 πn

Simplify

a = 2 arctan (\frac{1}{2}) + 2 πn

a = 2 arctan (\frac{1}{2}) + 2 πn

a = 2 arctan (\frac{1}{2}) + 2 πn

Show solutions in decimal form

a = 2 \cdot 0.46364 \dots + 2 πn

sin (x) = 0.731

sin (x) = 0.766

sin (x) = 0.755

3 tan^{2} (x) - 5 tan (x) + 2 = 0

θ, ρ = (4 sin (φ) cos (θ))

What is the general solution for tan(a/2)= 1/2 ?
The general solution for tan(a/2)= 1/2 is a=2*0.46364…+2pin