Question

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what is the value of \\(\tan 240^{\circ}\\)?

a. \\(\sqrt{2}\\)
b. \\(\sqrt{3}\\)
c. \\(\sqrt{4}\\)
d. \\(\sqrt{5}\\)

Explanation:

Identify the quadrant of the angle

The given angle is \(240^\circ\). Since \(180^\circ < 240^\circ < 270^\circ\), the terminal side lies in Quadrant III.

Determine the reference angle

Using the Tangent Ratio knowledge point

$$ \theta_{\text{ref}} = 240^\circ - 180^\circ = 60^\circ $$

Determine the sign in Quadrant III

In Quadrant III, both sine and cosine are negative, which means the tangent ratio is positive:

$$ \tan(240^\circ) = \tan(60^\circ) $$

Calculate the exact value

Using the Tangent Ratio knowledge point

$$ \tan(60^\circ) = \sqrt{3} $$

Answer:

• (A) \(\sqrt{2}\)
• (B) \(\sqrt{3}\) (Correct answer)
• (C) \(\sqrt{4}\)
• (D) \(\sqrt{5}\)