Find the Exact Value tan(660)

Problem

tan(660)

Solution

1. Find the coterminal angle by subtracting 360 from the given angle to bring it within the standard 0 to 360 range.

660−360=300

2. Determine the reference angle for 300 which is located in the fourth quadrant.

360−300=60

3. Identify the sign of the tangent function in the fourth quadrant. Since tangent is negative in the fourth quadrant, the result will be negative.

tan(300)=−tan(60)

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

tan(60)=√(,3)

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

tan(660)=−√(,3)

Final Answer

tan(660)=−√(,3)

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