If we always had to say
“the ratio of the height
to the hypotenuse”
and “the ratio of the
base
to the hypotenuse,”
it would just take too many words.
So, mathematicians have come up with two words to describe these ratios.

The ratio of the height
to the hypotenuse is called the
sine (pronounced like the word “sign”).

The ratio of the base to the
hypotenuse is called the
cosine (pronounced like “co-sign”).

Here is the same picture that you saw on the last page, with these new names.

Abbreviation and Pronunciation

The word sine is abbreviated as sin, but
it’s still pronounced “sign.” This is
really important. Your parents or friends will be interested to hear this:

I learned all about sin on the Internet today.

They will be shocked to hear you say this:

I learned all about sin on the Internet today.

The word cosine is abbreviated as cos
(but still pronounced
“co-sign”).
Luckily, you can’t get into trouble if you mispronounce it.