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Find the exact value of tangent, 240, degreestan240 ∘ in simplest form with a rational denominator

Question

Find the exact value of tangent, 240, degreestan240 ∘ in simplest form with a rational denominator

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Solution

To find the exact value of tan(240°), we can use the fact that the tangent function has a period of 180°. This means that tan(240°) = tan(240° - 180°) = tan(60°).

In the standard 30-60-90 right triangle, the tangent of 60° is √3. However, since 240° is in the third quadrant where tangent is positive, the value is -√3.

So, tan(240°) = -√3.

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