Find the Exact Value tan(270)

Problem

tan(270^∘)

Solution

1. Identify the angle on the unit circle. The angle 270^∘ is located on the negative y-axis.

2. Determine the coordinates (x,y) at 270^∘ On a unit circle, these coordinates are (0,−1)

3. Apply the definition of the tangent function. The tangent of an angle θ is defined as the ratio of the y-coordinate to the x-coordinate.

tan(θ)=y/x

4. Substitute the values into the formula.

tan(270^∘)=(−1)/0

5. Conclude that since division by zero is undefined, the tangent of 270^∘ does not exist.

Final Answer

tan(270^∘)=undefined

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