Find the Exact Value tan(30 degrees )

Problem

tan(30)

Solution

1. Identify the angle in the context of the unit circle or a special right triangle.

2. Recall the definition of the tangent function in terms of sine and cosine.

tan(θ)=sin(θ)/cos(θ)

3. Substitute the known values for the sine and cosine of 30

sin(30)=1/2

cos(30)=√(,3)/2

4. Calculate the ratio by dividing the two fractions.

tan(30)=1/2/√(,3)/2

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

tan(30)=1/√(,3)

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

tan(30)=(1⋅√(,3))/(√(,3)⋅√(,3))

tan(30)=√(,3)/3

Final Answer

tan(30)=√(,3)/3

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