Using standard trigonometric values, what is the exact value of tan 300°?

Introduction / Context:
This question checks your knowledge of tangent values for standard angles on the unit circle. The angle 300 degrees lies in the fourth quadrant, where tangent is negative. The reference angle is 60 degrees, whose tangent value is well known. This allows you to write tan 300° directly in terms of tan 60°.

Given Data / Assumptions:

• The angle is 300°.
• 300° = 360° - 60°.
• tan 60° = √3.
• In quadrant IV, sine is negative and cosine is positive, so tangent is negative.

Concept / Approach:
The tangent of an angle in the fourth quadrant can be related to its reference angle. In general, tan(360° - θ) = -tan θ. Using this identity with θ = 60°, we can quickly determine tan 300° without any complicated calculation. The result will involve the standard value tan 60° = √3.

Step-by-Step Solution:

Verification / Alternative check:
Another way is to use tan θ = sin θ / cos θ with known values of sin 300° and cos 300°. In the fourth quadrant, cos 300° = 1/2 and sin 300° = -√3/2. Then tan 300° = (sin 300°) / (cos 300°) = (-√3/2) / (1/2) = -√3, confirming the same result.

Why Other Options Are Wrong:

Common Pitfalls:
Students sometimes mix up sine, cosine, and tangent values for 30°, 45°, and 60°, or forget the sign change in different quadrants. Remembering that tangent is negative in quadrants II and IV and using the identity for tan(360° - θ) helps avoid these errors. Keeping a small table of special angle values in mind is very useful for such questions.

Final Answer:
-√3