Find the Exact Value tan(pi/6)

Problem

tan(π/6)

Solution

1. Identify the angle in degrees to better visualize the position on the unit circle.

π/6×180/π=30

2. Recall the coordinates of the point on the unit circle for the angle π/6

(x,y)=(√(,3)/2,1/2)

3. Apply the formula for the tangent function, which is the ratio of the y-coordinate to the x-coordinate.

tan(θ)=y/x

4. Substitute the known values into the formula.

tan(π/6)=1/2/√(,3)/2

5. Simplify the fraction by multiplying by the reciprocal of the denominator.

tan(π/6)=1/2×2/√(,3)

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

tan(π/6)=1/√(,3)×√(,3)/√(,3)

Final Answer

tan(π/6)=√(,3)/3

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