Evaluate tan(30 degrees )

Problem

tan(30^∘)

Solution

1. Identify the angle in the context of the unit circle or a special right triangle. The angle 30^∘ corresponds to the radian measure π/6

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 sin(30^∘) and cos(30^∘)

sin(30^∘)=1/2

cos(30^∘)=√(,3)/2

4. Calculate the ratio by dividing the two values.

tan(30^∘)=1/2/√(,3)/2

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

tan(30^∘)=1/√(,3)

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

tan(30^∘)=√(,3)/3

Final Answer

tan(30^∘)=√(,3)/3

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