Simplify tan((3pi)/4)

Problem

tan((3*π)/4)

Solution

1. Identify the angle (3*π)/4 on the unit circle. This angle is in the second quadrant.

2. Determine the reference angle by subtracting the angle from π

Reference Angle=π−(3*π)/4=π/4

3. Apply the tangent value for the reference angle.

tan(π/4)=1

4. Determine the sign of the tangent function in the second quadrant. Since tan(θ)=sin(θ)/cos(θ) and cosine is negative while sine is positive in the second quadrant, the tangent value must be negative.

tan((3*π)/4)=−1

Final Answer

tan((3*π)/4)=−1

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