Find the Exact Value tan((5pi)/4)

Problem

tan((5*π)/4)

Solution

1. Identify the quadrant of the angle (5*π)/4 Since π<(5*π)/4<(3*π)/2 the angle lies in Quadrant III.

2. Determine the reference angle (θ_r*e*ƒ) by subtracting π from the given angle.

(θ_r*e*ƒ)=(5*π)/4−π

(θ_r*e*ƒ)=π/4

3. Apply the sign of the tangent function in Quadrant III. In Quadrant III, the tangent of an angle is positive.

tan((5*π)/4)=tan(π/4)

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

tan(π/4)=1

Final Answer

tan((5*π)/4)=1

Want more problems? Check here!