Find the Exact Value tan(0 degrees )

Problem

tan(0^∘)

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 0^∘ into the trigonometric functions.

tan(0^∘)=sin(0^∘)/cos(0^∘)

3. Evaluate the sine and cosine of 0^∘ using the unit circle, where the coordinates at 0^∘ are (1,0)

sin(0^∘)=0

cos(0^∘)=1

4. Simplify the fraction by dividing the values.

tan(0^∘)=0/1

tan(0^∘)=0

Final Answer

tan(0^∘)=0

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