Exact value of tan 90°

Step by step

The question

Question: find the exact value of tan 90°.

1 Draw the unit circle

The unit circle has its center at 0 and radius 1.

We turn 90° from the positive x-axis, against the clock.

The ray meets the circle at the point P.

Here is the key fact.

P is the point (cos 90°, sin 90°).

Across is cos.

Up is sin.

2 Read the point

P is on the y-axis, one step from the center: up.

So P = (0, 1).

Careful!

Tan is sin over cos: the up number divided by the across number.

3 Divide

Tan is sin over cos: up divided by across.

Now put the numbers in: sin 90° = 1 and cos 90° = 0.

But the bottom is 0.

We can never divide by 0.

So tan 90° has no answer: it is undefined.

Let's look back.

First: draw the unit circle.

Then: read the point.

Last: divide.