Find the Exact Value tan(180 degrees )

Problem

tan(180^∘)

Solution

1. Identify the definition of the tangent function in terms of the unit circle coordinates (x,y)

tan(θ)=y/x

2. Determine the coordinates on the unit circle corresponding to an angle of 180^∘

(x,y)=(−1,0)

3. Substitute the values of x=−1 and y=0 into the tangent formula.

tan(180^∘)=0/(−1)

4. Simplify the fraction to find the exact value.

tan(180^∘)=0

Final Answer

tan(180^∘)=0

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