Use the given triangles to evaluate each expression. If necessary, express the value without a square root in the denominator by rationalizing the denominator.


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tan 𝜋/3

Key Concepts

Tangent Function

The tangent function, denoted as tan(θ), is a fundamental trigonometric function defined as the ratio of the opposite side to the adjacent side in a right triangle. It can also be expressed in terms of sine and cosine as tan(θ) = sin(θ)/cos(θ). Understanding this function is crucial for evaluating expressions involving angles.

Special Angles in Trigonometry

In trigonometry, special angles such as 0°, 30°, 45°, 60°, and 90° have known sine, cosine, and tangent values. For example, tan(π/3) corresponds to 60°, where the tangent value is √3. Familiarity with these special angles allows for quick evaluations of trigonometric expressions.

Rationalizing the Denominator

Rationalizing the denominator is a technique used to eliminate square roots or irrational numbers from the denominator of a fraction. This is achieved by multiplying the numerator and denominator by a suitable value that will result in a rational number in the denominator. This process is often required in trigonometric evaluations to present answers in a standard form.