Find the Exact Value tan(270 degrees )

Problem

tan(270)

Solution

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

tan(θ)=sin(θ)/cos(θ)

2. Determine the coordinates of the angle 270 on the unit circle.

(x,y)=(0,−1)

3. Evaluate the sine and cosine values at 270 based on the unit circle coordinates.

sin(270)=−1

cos(270)=0

4. Substitute these values into the tangent formula.

tan(270)=(−1)/0

5. Conclude that since division by zero is not defined, the value does not exist.

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Final Answer

tan(270)=undefined

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