Find the Exact Value tan(pi/3)

Problem

tan(π/3)

Solution

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

π/3* radians=60

2. Recall the coordinates (x,y) for the angle π/3 on the unit circle.

x=cos(π/3)=1/2

y=sin(π/3)=√(,3)/2

3. Apply the formula for the tangent function, which is the ratio of the sine to the cosine.

tan(θ)=sin(θ)/cos(θ)

4. Substitute the known values into the ratio.

tan(π/3)=√(,3)/2/1/2

5. Simplify the fraction by canceling the common denominator of 2

tan(π/3)=√(,3)

Final Answer

tan(π/3)=√(,3)

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