Find the Exact Value tan(-240 degrees )

Problem

tan(−240)

Solution

1. Find the coterminal angle by adding 360 to the negative angle to locate it within the standard 0 to 360 range.

θ=−240+360=120

2. Identify the quadrant for 120 Since 90<120<180 the angle lies in Quadrant II.

3. Determine the reference angle θ′ for an angle in Quadrant II using the formula θ′=180−θ

θ′=180−120=60

4. Determine the sign of the tangent function in Quadrant II. In Quadrant II, sine is positive while cosine and tangent are negative.

tan(120)=−tan(60)

5. Evaluate the tangent of the reference angle using known trigonometric values.

tan(60)=√(,3)

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

tan(−240)=−√(,3)

Final Answer

tan(−240)=−√(,3)

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