Find the Exact Value tan(135 degrees )

Problem

tan(135^∘)

Solution

1. Identify the angle in the coordinate plane. The angle 135^∘ is located in the second quadrant.

2. Determine the reference angle. Since 135^∘ is in the second quadrant, the reference angle is calculated as 180^∘−135^∘=45^∘

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

4. Evaluate the tangent of the reference angle. We know that tan(45^∘)=1

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

Final Answer

tan(135^∘)=−1

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