Simplify tan(180)

Problem

tan(180^∘)

Solution

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

tan(θ)=sin(θ)/cos(θ)

2. Substitute the given angle 180^∘ into the trigonometric functions.

tan(180^∘)=sin(180^∘)/cos(180^∘)

3. Evaluate the sine and cosine values at 180^∘ using the unit circle.

sin(180^∘)=0

cos(180^∘)=−1

4. Simplify the resulting fraction.

0/(−1)=0

Final Answer

tan(180^∘)=0

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