Find the Value Using the Unit Circle tan(60 degrees )

Problem

tan(60)

Solution

1. Identify the coordinates on the unit circle for the angle 60

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

3. Determine the values for 60 which are x=1/2 and y=√(,3)/2

4. Apply the formula for the tangent function, which is defined as the ratio of the ycoordinate to the xcoordinate.

tan(θ)=y/x

5. Substitute the values into the formula.

tan(60)=√(,3)/2/1/2

6. Simplify the expression by canceling the denominators.

tan(60)=√(,3)

Final Answer

tan(60)=√(,3)

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