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

Problem

tan(−(3*π)/4)

Solution

1. Identify the property of the tangent function for negative angles, which is tan(−θ)=−tan(θ)

tan(−(3*π)/4)=−tan((3*π)/4)

2. Determine the reference angle for (3*π)/4 Since the angle is in the second quadrant, the reference angle is π−(3*π)/4=π/4

Reference Angle=π/4

3. Evaluate the tangent of the reference angle.

tan(π/4)=1

4. Determine the sign of the tangent function in the second quadrant. In the second quadrant, tangent is negative.

tan((3*π)/4)=−1

5. Substitute the value back into the expression from step 1.

−(−1)=1

Final Answer

tan(−(3*π)/4)=1

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