What is the value of tan(pi+pi/3) ?

The value of tan(pi+pi/3) is square root of 3

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tan(pi+pi/3)

tan (π + \frac{π}{3})

3

Decimal Notation

1.73205 \dots

Solution steps

tan (π + \frac{π}{3})

Simplify:

π + \frac{π}{3} = \frac{4 π}{3}

π + \frac{π}{3}

Convert element to fraction:

π = \frac{π 3}{3}

= \frac{π 3}{3} + \frac{π}{3}

Since the denominators are equal, combine the fractions:

\frac{a}{c} \pm \frac{b}{c} = \frac{a \pm b}{c}

= \frac{π 3 + π}{3}

Add similar elements:

3 π + π = 4 π

= \frac{4 π}{3}

= tan (\frac{4 π}{3})

tan (\frac{4 π}{3}) = tan (\frac{π}{3})

tan (\frac{4 π}{3})

Rewrite

\frac{4 π}{3}

π + \frac{π}{3}

= tan (π + \frac{π}{3})

Apply the periodicity of

tan

tan (x + π) = tan (x)

tan (π + \frac{π}{3}) = tan (\frac{π}{3})

= tan (\frac{π}{3})

= tan (\frac{π}{3})

Use the following trivial identity:

tan (\frac{π}{3}) = 3

tan (\frac{π}{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}

= 3

= 3

6 sin^{2} (x) - 5 sin (x) = 0

sinh (4 x) = \frac{3}{4}

tan (x) + sec (x) = 3

cos^{2} (3 x + \frac{π}{4}) = \frac{3}{4}

2 sin (\frac{π}{3} - x) - 1 = 0

What is the value of tan(pi+pi/3) ?
The value of tan(pi+pi/3) is square root of 3