Find the Exact Value tan(30)

Problem

tan(30)

Solution

1. Identify the definition of the tangent function in terms of sine and cosine.

tan(θ)=sin(θ)/cos(θ)

2. Recall the exact values for sine and cosine at 30 from the unit circle.

sin(30)=1/2

cos(30)=√(,3)/2

3. Substitute these values into the tangent ratio.

tan(30)=1/2/√(,3)/2

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

tan(30)=1/2⋅2/√(,3)

tan(30)=1/√(,3)

5. 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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