Exact value of cos 180°

Step by step

The question

Question: find the exact value of cos 180°.

1 Draw the unit circle

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

We turn 180° 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 180°, sin 180°).

Across is cos.

Up is sin.

2 Read the point

P is on the x-axis, one step from the center: left.

So P = (−1, 0).

Careful!

The first number of the point is cos.

The second is sin.

Not the other way round.

Cos is the across number.

So cos 180° = −1.

3 Check

Let's check with the calculator: cos 180°.

The calculator says −1 too.

So it is right!

Let's look back.

First: draw the unit circle.

Then: read the point.

Last: check.