Question

The terminal point of theta is (0, 1). What is tan theta?

Answer 1

The terminal point of an angle is (0,1), and we are asked to determine the tangent of the said angle. We can exemplify the problem in the following diagram.

Even though the point (0,1) lies in the y-axis, the idea if the diagram is to show that the terminal point of an angle represents the values of the adjacent and opposite sides of a triangle. Therefore, in the given terminal point the triangle has adjacent side 0 and opposite side 1. Now let's remember the definition of the function tangent:

`\tan \theta=(opposite)/(adjacent)`

Replacing the values we get:

`\tan \theta=(1)/(0)`

Because we have a division by zero the function tangent of theta is undefined for this terminal point.