Find the Exact Value tan(300 degrees )

Problem

tan(300)

Solution

1. Identify the reference angle by finding the distance to the nearest x-axis. Since 300 is in the fourth quadrant, subtract it from 360

(θ_ref)=360−300=60

2. Determine the sign of the tangent function in the fourth quadrant. In the fourth quadrant, cosine is positive while sine and tangent are negative.

tan(300)=−tan(60)

3. Evaluate the tangent of the reference angle using known trigonometric values for special angles.

tan(60)=√(,3)

4. Combine the sign and the value to find the final result.

tan(300)=−√(,3)

Final Answer

tan(300)=−√(,3)

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