Find the Exact Value tan((5pi)/3)

Problem

tan((5*π)/3)

Solution

1. Identify the quadrant of the angle (5*π)/3 Since (3*π)/2<(5*π)/3<2*π the angle is in the fourth quadrant.

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

(θ_r*e*ƒ)=2*π−(5*π)/3

(θ_r*e*ƒ)=π/3

3. Recall the tangent value for the reference angle π/3

tan(π/3)=√(,3)

4. Apply the sign for the fourth quadrant. In the fourth quadrant, the tangent function is negative.

tan((5*π)/3)=−tan(π/3)

tan((5*π)/3)=−√(,3)

Final Answer

tan((5*π)/3)=−√(,3)

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