What is the general solution for tan(2θ)=0.4 ?

The general solution for tan(2θ)=0.4 is θ=(0.38050…)/2+(pin)/2

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tan(2θ)=0.4

tan (2 θ) = 0.4

θ = \frac{0.38050 \dots}{2} + \frac{πn}{2}

Degrees

θ = 10.90070 \dots^{\circ} + 9 0^{\circ} n

Solution steps

tan (2 θ) = 0.4

Apply trig inverse properties

tan (2 θ) = 0.4

General solutions for

tan (2 θ) = 0.4

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

2 θ = arctan (0.4) + πn

2 θ = arctan (0.4) + πn

Solve

2 θ = arctan (0.4) + πn : θ = \frac{arctan ( 0.4 )}{2} + \frac{πn}{2}

2 θ = arctan (0.4) + πn

Divide both sides by

2

2 θ = arctan (0.4) + πn

Divide both sides by

2

\frac{2 θ}{2} = \frac{arctan ( 0.4 )}{2} + \frac{πn}{2}

Simplify

θ = \frac{arctan ( 0.4 )}{2} + \frac{πn}{2}

θ = \frac{arctan ( 0.4 )}{2} + \frac{πn}{2}

θ = \frac{arctan ( 0.4 )}{2} + \frac{πn}{2}

Show solutions in decimal form

θ = \frac{0.38050 \dots}{2} + \frac{πn}{2}

csc (\frac{θ}{2}) = sin (\frac{θ}{2})

sin (3 x) = - 1, 0 \leq x \leq 2 π

sin (θ) = 0.25

3 0^{2} = 2 0^{2} + 1 8^{2} - 2 (20) (18) cos (A)

cos (x) = \frac{308}{1475}

What is the general solution for tan(2θ)=0.4 ?
The general solution for tan(2θ)=0.4 is θ=(0.38050…)/2+(pin)/2