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

The general solution for tan(x)= 3/(sqrt(3)) is x= pi/3+pin

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tan(x)= 3/(sqrt(3))

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

x = \frac{π}{3} + πn

Solution steps

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

Simplify

\frac{3}{3} : 3

\frac{3}{3}

Apply radical rule:

3 = 3^{\frac{1}{2}}

= \frac{3}{3 ^{\frac{1}{2}}}

Apply exponent rule:

\frac{x ^{a}}{x ^{b}} = x^{a - b}

\frac{3 ^{1}}{3 ^{\frac{1}{2}}} = 3^{1 - \frac{1}{2}}

= 3^{1 - \frac{1}{2}}

Subtract the numbers:

1 - \frac{1}{2} = \frac{1}{2}

= 3^{\frac{1}{2}}

Apply radical rule:

3^{\frac{1}{2}} = 3

= 3

General solutions for

tan (x) = 3

tan (x)

periodicity table with

πn

cycle:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} tan (x) 0 \frac{3}{3} 13 \pm \infty - 3 - 1 - \frac{3}{3}

x = \frac{π}{3} + πn

x = \frac{π}{3} + πn

6 (1 - cos (θ)) = sin^{2} (θ)

25 tan^{2} (θ) - 9 = 0

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

8 cos^{2} (x) + 6 cos (x) + 1 = 0

3 arctan (x) = π

What is the general solution for tan(x)= 3/(sqrt(3)) ?
The general solution for tan(x)= 3/(sqrt(3)) is x= pi/3+pin