Evaluate tan((7pi)/6)

Problem

tan((7*π)/6)

Solution

1. Identify the quadrant of the angle (7*π)/6 Since π<(7*π)/6<(3*π)/2 the angle is in the third quadrant.

2. Determine the reference angle. The reference angle (θ_r*e*ƒ) is calculated as (7*π)/6−π

(θ_r*e*ƒ)=π/6

3. Apply the sign of the tangent function in the third quadrant. In the third quadrant, tangent is positive.

tan((7*π)/6)=tan(π/6)

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

tan(π/6)=1/√(,3)

5. Rationalize the denominator by multiplying the numerator and denominator by √(,3)

1/√(,3)⋅√(,3)/√(,3)=√(,3)/3

Final Answer

tan((7*π)/6)=√(,3)/3

Want more problems? Check here!