Find the Value Using the Unit Circle tan((3pi)/2)

Problem

tan((3*π)/2)

Solution

1. Identify the angle on the unit circle. The angle (3*π)/2 radians corresponds to 270 which is located on the negative y-axis.

2. Determine the coordinates (x,y) at this angle. On the unit circle, the point at (3*π)/2 is (0,−1)

3. Apply the formula for the tangent function in terms of coordinates.

tan(θ)=y/x

4. Substitute the values x=0 and y=−1 into the formula.

tan((3*π)/2)=(−1)/0

5. Conclude that since division by zero is not allowed in mathematics, the value is undefined.

Final Answer

tan((3*π)/2)=undefined

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