Simplify tan((5pi)/4)

Problem

tan((5*π)/4)

Solution

1. Identify the angle (5*π)/4 on the unit circle.

2. Determine the quadrant of the angle. Since π<(5*π)/4<(3*π)/2 the angle is in the third quadrant.

3. Find the reference angle by subtracting π from the given angle.

(θ_ref)=(5*π)/4−π

(θ_ref)=π/4

4. Apply the property that the tangent function is positive in the third quadrant.

tan((5*π)/4)=tan(π/4)

5. Evaluate the tangent of the reference angle using known trigonometric values.

tan(π/4)=1

Final Answer

tan((5*π)/4)=1

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