What is the general solution for tan(2x)=0.6 ?

The general solution for tan(2x)=0.6 is x=(0.54041…)/2+(pin)/2

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tan(2x)=0.6

tan (2 x) = 0.6

x = \frac{0.54041 \dots}{2} + \frac{πn}{2}

Degrees

x = 15.48187 \dots^{\circ} + 9 0^{\circ} n

Solution steps

tan (2 x) = 0.6

Apply trig inverse properties

tan (2 x) = 0.6

General solutions for

tan (2 x) = 0.6

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

2 x = arctan (0.6) + πn

2 x = arctan (0.6) + πn

Solve

2 x = arctan (0.6) + πn : x = \frac{arctan ( 0.6 )}{2} + \frac{πn}{2}

2 x = arctan (0.6) + πn

Divide both sides by

2

2 x = arctan (0.6) + πn

Divide both sides by

2

\frac{2 x}{2} = \frac{arctan ( 0.6 )}{2} + \frac{πn}{2}

Simplify

x = \frac{arctan ( 0.6 )}{2} + \frac{πn}{2}

x = \frac{arctan ( 0.6 )}{2} + \frac{πn}{2}

x = \frac{arctan ( 0.6 )}{2} + \frac{πn}{2}

Show solutions in decimal form

x = \frac{0.54041 \dots}{2} + \frac{πn}{2}

2 sin (3 θ) = - 1

2 + 2 cos (θ) = 2 - 2 cos (θ)

1 + 4 sin (x) = 0

cos^{2} (x) = \frac{3}{2} sin (x)

sin (x) = cos (\frac{x}{2})

What is the general solution for tan(2x)=0.6 ?
The general solution for tan(2x)=0.6 is x=(0.54041…)/2+(pin)/2