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sine and cosine

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.

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

[Hear it] 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.


[Applet appears here for Java-capable browsers]

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:

[Hear it] I learned all about sin on the Internet today.

They will be shocked to hear you say this:

[Hear it] 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.

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