What is the general solution for tan(6t)=2 ?

The general solution for tan(6t)=2 is t=(1.10714…)/6+(pin)/6

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tan(6t)=2

tan (6 t) = 2

t = \frac{1.10714 \dots}{6} + \frac{πn}{6}

Degrees

t = 10.57249 \dots^{\circ} + 3 0^{\circ} n

Solution steps

tan (6 t) = 2

Apply trig inverse properties

tan (6 t) = 2

General solutions for

tan (6 t) = 2

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

6 t = arctan (2) + πn

6 t = arctan (2) + πn

Solve

6 t = arctan (2) + πn : t = \frac{arctan ( 2 )}{6} + \frac{πn}{6}

6 t = arctan (2) + πn

Divide both sides by

6

6 t = arctan (2) + πn

Divide both sides by

6

\frac{6 t}{6} = \frac{arctan ( 2 )}{6} + \frac{πn}{6}

Simplify

t = \frac{arctan ( 2 )}{6} + \frac{πn}{6}

t = \frac{arctan ( 2 )}{6} + \frac{πn}{6}

t = \frac{arctan ( 2 )}{6} + \frac{πn}{6}

Show solutions in decimal form

t = \frac{1.10714 \dots}{6} + \frac{πn}{6}

sin (2 x) - sin (x) + cos (2 x) + cos (x) = 0

(cos (x) = 1) = (sec (x) = 1)

cot (\frac{x}{3}) = \frac{- 1}{3}

cos^{2} (θ) = sin^{2} (θ) + 1, 0^{\circ} \leq θ \leq 36 0^{\circ}

tan (2 x) (1 - tan^{2} (x)) = \frac{2}{3}

What is the general solution for tan(6t)=2 ?
The general solution for tan(6t)=2 is t=(1.10714…)/6+(pin)/6