Find the Exact Value tan(-pi/6)

Problem

tan(−π/6)

Solution

1. Identify the property of the tangent function for negative angles. Since tangent is an odd function, tan(−θ)=−tan(θ)

tan(−π/6)=−tan(π/6)

2. Determine the value of tan(π/6) using the unit circle or special triangles.

tan(π/6)=sin(π/6)/cos(π/6)

3. Substitute the known values sin(π/6)=1/2 and cos(π/6)=√(,3)/2

tan(π/6)=(1/2)/(√(,3)/2)

4. Simplify the fraction.

tan(π/6)=1/√(,3)

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

tan(π/6)=√(,3)/3

6. Apply the negative sign from the first step to find the final value.

tan(−π/6)=−√(,3)/3

Final Answer

tan(−π/6)=−√(,3)/3

Want more problems? Check here!