Find the Exact Value tan(135)

Problem

tan(135)

Solution

1. Identify the angle's position on the unit circle. The angle 135 is located in the second quadrant.

2. Determine the reference angle. Subtract the angle from 180 to find the reference angle in the second quadrant.

180−135=45

3. Apply the tangent property for the second quadrant. In the second quadrant, the tangent function is negative.

tan(135)=−tan(45)

4. Substitute the known exact value for the tangent of the reference angle. The value of tan(45) is 1

tan(135)=−1

Final Answer

tan(135)=−1

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