Find the Exact Value tan((3pi)/4)

Problem

tan((3*π)/4)

Solution

1. Identify the quadrant of the angle (3*π)/4 Since π/2<(3*π)/4<π the angle lies in the second quadrant.

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

(θ_ref)=π−(3*π)/4

(θ_ref)=π/4

3. Recall the tangent value for the reference angle π/4

tan(π/4)=1

4. Apply the sign for the second quadrant. In the second quadrant, the tangent function is negative.

tan((3*π)/4)=−1

Final Answer

tan((3*π)/4)=−1

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