Find the Value Using the Unit Circle tan(60)

Problem

tan(60)

Solution

1. Identify the coordinates on the unit circle for the angle 60 At 60 (or π/3 radians), the coordinates (x,y) are (1/2,√(,3)/2)

2. Apply the formula for the tangent function in terms of the unit circle coordinates, where tan(θ)=y/x

3. Substitute the values x=1/2 and y=√(,3)/2 into the formula.

tan(60)=√(,3)/2/1/2

4. Simplify the fraction by multiplying the numerator by the reciprocal of the denominator.

tan(60)=√(,3)/2⋅2/1

tan(60)=√(,3)

Final Answer

tan(60)=√(,3)

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