Tag Archives: Pencil

Let’s take a look at this pic below

Now as the angle x goes down and down toward 0, the side on the front of the angle also get shorten and shorten. When x goes negative the side in front of the angle point downward.

The side near the angle remain constant though.

As x goes down to exactly -x we got a congruent triangle except flipped outside down.

So the cosine remain the same, namely b/c. The sine is just the additive inverse. Before it’s a/c, now it’s -a/c.
Hence, we easily see sin(-x)=-sin(x) and cos(-x)= cos(x)