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

The general solution for 3tan(4x)=2 is x=(0.58800…)/4+(pin)/4

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3tan(4x)=2

3 tan (4 x) = 2

x = \frac{0.58800 \dots}{4} + \frac{πn}{4}

Degrees

x = 8.42251 \dots^{\circ} + 4 5^{\circ} n

Solution steps

3 tan (4 x) = 2

Divide both sides by

3

3 tan (4 x) = 2

Divide both sides by

3

\frac{3 tan ( 4 x )}{3} = \frac{2}{3}

Simplify

tan (4 x) = \frac{2}{3}

tan (4 x) = \frac{2}{3}

Apply trig inverse properties

tan (4 x) = \frac{2}{3}

General solutions for

tan (4 x) = \frac{2}{3}

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

4 x = arctan (\frac{2}{3}) + πn

4 x = arctan (\frac{2}{3}) + πn

Solve

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

4 x = arctan (\frac{2}{3}) + πn

Divide both sides by

4

4 x = arctan (\frac{2}{3}) + πn

Divide both sides by

4

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

Simplify

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

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

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

Show solutions in decimal form

x = \frac{0.58800 \dots}{4} + \frac{πn}{4}

- cos (2 x) = 0

tan (2 x) = - \frac{3}{3}

2 cot^{2} (x) - 3 csc (x) = 0

3 - 4 cos^{2} (x) = 0

sin (2 θ) = - \frac{1}{2}, 0 \leq θ \leq 2 π

What is the general solution for 3tan(4x)=2 ?
The general solution for 3tan(4x)=2 is x=(0.58800…)/4+(pin)/4