Find the Exact Value tan(60 degrees )

Problem

tan(60^∘)

Solution

1. Identify the angle on the unit circle. The angle 60^∘ corresponds to the point (x,y)=(1/2,√(,3)/2)

2. Apply 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(60^∘) and cos(60^∘)

sin(60^∘)=√(,3)/2

cos(60^∘)=1/2

4. Simplify the resulting fraction by canceling the common denominator.

tan(60^∘)=√(,3)/2/1/2

tan(60^∘)=√(,3)

Final Answer

tan(60^∘)=√(,3)

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