What is the general solution for tan(3x)=5 ?

The general solution for tan(3x)=5 is x=(1.37340…)/3+(pin)/3

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tan(3x)=5

tan (3 x) = 5

x = \frac{1.37340 \dots}{3} + \frac{πn}{3}

Solution steps

tan (3 x) = 5

Apply trig inverse properties

3 x = arctan (5) + πn

Solve

3 x = arctan (5) + πn : x = \frac{arctan ( 5 )}{3} + \frac{πn}{3}

x = \frac{arctan ( 5 )}{3} + \frac{πn}{3}

Show solutions in decimal form

x = \frac{1.37340 \dots}{3} + \frac{πn}{3}

x, cos (x) - sin (x) = 0

tan (θ) = 2 sin (θ)

0 = - sin (x) + cos (x)

sin (3 θ) = \frac{1}{2}

- sin^{2} (θ) + cos^{2} (θ) = 1 - sin (θ)

What is the general solution for tan(3x)=5 ?
The general solution for tan(3x)=5 is x=(1.37340…)/3+(pin)/3