Find the Value Using the Unit Circle tan(30 degrees )

Problem

tan(30)

Solution

1. Identify the coordinates on the unit circle for the given angle 30

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

3. Determine the values for 30 which are x=√(,3)/2 and y=1/2

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

5. Substitute the values into the formula:

tan(30)=1/2/√(,3)/2

6. Simplify the complex fraction by multiplying by the reciprocal:

tan(30)=1/2⋅2/√(,3)

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

tan(30)=1/√(,3)⋅√(,3)/√(,3)

Final Answer

tan(30)=√(,3)/3

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