Simplify tan((7pi)/4)

Problem

tan((7*π)/4)

Solution

1. Identify the angle (7*π)/4 on the unit circle. This angle is in the fourth quadrant.

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

Reference Angle=2*π−(7*π)/4

Reference Angle=π/4

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

tan(π/4)=1

4. Determine the sign of the tangent function in the fourth quadrant. In the fourth quadrant, the xcoordinate (cosine) is positive and the ycoordinate (sine) is negative, so the tangent is negative.

tan((7*π)/4)=−1

Final Answer

tan((7*π)/4)=−1

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