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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