Find the Exact Value tan((7pi)/4)

Problem

tan((7*π)/4)

Solution

1. Identify the angle (7*π)/4 on the unit circle.

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

Reference Angle=2*π−(7*π)/4

Reference Angle=π/4

3. Determine the quadrant of the angle. Since (3*π)/2<(7*π)/4<2*π the angle lies in Quadrant IV.

4. Determine the sign of the tangent function in Quadrant IV. In this quadrant, x is positive and y is negative, so tan(θ)=y/x is negative.

5. Apply the reference angle value. The value of tan(π/4) is 1

6. Combine the value with the correct sign.

tan((7*π)/4)=−1

Final Answer

tan((7*π)/4)=−1

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