Find the Value Using the Unit Circle tan(pi/3)

Problem

tan(π/3)

Solution

1. Identify the coordinates on the unit circle for the angle θ=π/3

2. Recall that for any angle θ the coordinates (x,y) are (cos(θ),sin(θ))

3. Determine the values from the unit circle: cos(π/3)=1/2 and sin(π/3)=√(,3)/2

4. Apply the formula for the tangent function, which is tan(θ)=sin(θ)/cos(θ)

5. Substitute the values into the formula: tan(π/3)=√(,3)/2/1/2

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

Final Answer

tan(π/3)=√(,3)

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