What is the general solution for tan(2θ)= 4/3 ?

The general solution for tan(2θ)= 4/3 is θ=(0.92729…)/2+(pin)/2

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tan(2θ)= 4/3

tan (2 θ) = \frac{4}{3}

θ = \frac{0.92729 \dots}{2} + \frac{πn}{2}

Degrees

θ = 26.56505 \dots^{\circ} + 9 0^{\circ} n

Solution steps

tan (2 θ) = \frac{4}{3}

Apply trig inverse properties

tan (2 θ) = \frac{4}{3}

General solutions for

tan (2 θ) = \frac{4}{3}

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

2 θ = arctan (\frac{4}{3}) + πn

2 θ = arctan (\frac{4}{3}) + πn

Solve

2 θ = arctan (\frac{4}{3}) + πn : θ = \frac{arctan ( \frac{4}{3} )}{2} + \frac{πn}{2}

2 θ = arctan (\frac{4}{3}) + πn

Divide both sides by

2

2 θ = arctan (\frac{4}{3}) + πn

Divide both sides by

2

\frac{2 θ}{2} = \frac{arctan ( \frac{4}{3} )}{2} + \frac{πn}{2}

Simplify

θ = \frac{arctan ( \frac{4}{3} )}{2} + \frac{πn}{2}

θ = \frac{arctan ( \frac{4}{3} )}{2} + \frac{πn}{2}

θ = \frac{arctan ( \frac{4}{3} )}{2} + \frac{πn}{2}

Show solutions in decimal form

θ = \frac{0.92729 \dots}{2} + \frac{πn}{2}

3 sec^{2} (x) + 2 - 8 tan (x) = 0

cos (θ) - 1 = cos (2 θ)

5 tan (x) = 9 sin (x)

x, sin (\frac{π x}{4}) = y - 1

sin (θ) = \frac{12}{37}

What is the general solution for tan(2θ)= 4/3 ?
The general solution for tan(2θ)= 4/3 is θ=(0.92729…)/2+(pin)/2