What is the value of tan(-(7pi)/3) ?

The value of tan(-(7pi)/3) is -sqrt(3)

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tan(-(7pi)/3)

tan (- \frac{7 π}{3})

- 3

Decimal Notation

- 1.73205 \dots

Solution steps

tan (- \frac{7 π}{3})

Use the following property:

tan (- x) = - tan (x)

tan (- \frac{7 π}{3}) = - tan (\frac{7 π}{3})

= - tan (\frac{7 π}{3})

tan (\frac{7 π}{3}) = tan (\frac{π}{3})

tan (\frac{7 π}{3})

Rewrite

\frac{7 π}{3}

π \cdot 2 + \frac{π}{3}

= tan (π 2 + \frac{π}{3})

Apply the periodicity of

tan

tan (x + π \cdot k) = tan (x)

tan (π \cdot 2 + \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

15 \cdot cos (6 0^{\circ})

6 cos (16 0^{\circ})

arctan (tan (\frac{π}{2}))

sin (58 5^{\circ})

csc (1 0^{\circ})