# Find the exact value of tan (pi/3)

Trigonometry is a branch of mathematics that deals with the relation between the angles and sides of a triangle. There are a total of six trignometric ratios.

## Answer: The exact value of tan (pi/3) is ⎷3

Let us see, how to solve.

**Explanation:**

We are using a trigonometric relation, tanθ = sinθ/cosθ, to find the value of tan (pi/3).

We are using a reference triangle to calculate the values of sine and cosine.

Since, θ = pi/3, therefore

sin(pi/3) = ⎷3/2, and

cos(pi/3) = 1/2

Now substitute sin(pi/3) = ⎷3/2, and cos(pi/3) = 1/2 in the equation tanθ = sinθ/cosθ

tanθ = sinθ/cosθ

tan(pi/3) = sin(pi/3)/cos(pi/3)

tan(pi/3) = (⎷3/2)/(1/2)

= ⎷3

### Thus, the exact value of tan (pi/3) is ⎷3

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