Trigonometry is greek for <em>triangle measurement</em>.
Three of the most basic ideas in trigonometry are the <em>sine</em>, <em>cosine</em>, and <em>tangent ratios</em>. The sine, cosine, and tangent ratios can be defined as follows.
I have attached right triangle ABC in the image attached.
In right triangle ABC, the sine of angle A is equal to the ratio of the length of the side opposite angle A to the length of the hypotenuse. So in right triangle ABC, the sine of angle A equals y over z. The abbreviation we use for sine is <u>sin</u>.
Next, the cosine of angle A is equal to the ratio of the length of the side adjacent to angle A to the length of the hypotenuse. So in right triangle ABC, the cosine of angle A equals x over z. The abbreviation we use for cosine is <u>cos</u>.
Finally, the tangent of angle A is equal to the ratio of the length of the side opposite angle A to the length of the side adjacent to angle A. So in right triangle ABC, the tangent of angle A equals y over x. The abbreviation we use for tangent is <u>tan</u>.
An easy way to remember the sine, cosine, and tangent ratios is to use the word SOH-CAH-TOA.
<em>Sine is opposite over hypotenuse, cosine is adjacent over hypotenuse, and tangent is opposite over adjacent.</em>