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

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

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tan(-pi/3)

tan (- \frac{π}{3})

- 3

Decimal Notation

- 1.73205 \dots

Solution steps

tan (- \frac{π}{3})

Use the following property:

tan (- x) = - tan (x)

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

sec (θ) - tan (θ) = \frac{cos ( θ )}{1 + sin ( θ )}

cos (3 x) = - 1

tan (θ) = - 1

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

sin (x) + cos (x) = 2