# Trigonometric Ratios

"The word Trignometry is formed from greek language. Trigon means triangle and metric means measurement. The trigonometric ratios are special measurements of a right triangle (a triangle with one angle measuring 90°90° ). Remember that the two sides of a right triangle which form the right angle are called the legs, and the third side (opposite the right angle) is called the hypotenuse .

There are three basic trigonometric ratios: sinecosine, and tangent. Given a right triangle, you can find the sine (or cosine, or tangent) of either of the non- 90° angles.

Example:

Write expressions for the sine, cosine, and tangent of ∠A∠A .

The length of the leg opposite ∠A∠A is aa. The length of the leg adjacent to ∠A∠A is bb, and the length of the hypotenuse is cc.

The sine of the angle is given by the ratio "opposite over hypotenuse." So,

sin∠A=acsin∠A=ac

The cosine is given by the ratio "adjacent over hypotenuse."

cos∠A=bccos∠A=bc

The tangent is given by the ratio "opposite over adjacent."

tan∠A=abtan∠A=ab

Generations of students have used the mnemonic "SOHCAHTOA" to remember which ratio is which. ( ine: pposite over Hypotenuse, osine: djacent over ypotenuse, angent: pposite over djacent.)

Other Trigonometric Ratios

The other common trigonometric ratios are:

Example:

Write expressions for the secant, cosecant, and cotangent of ∠A∠A .

The length of the leg opposite ∠A∠A is aa. The length of the leg adjacent to ∠A∠A is bb, and the length of the hypotenuse is cc.

The secant of the angle is given by the ratio "hypotenuse over adjacent". So,

sec∠A=cbsec∠A=cb

The cosecant is given by the ratio "hypotenuse over opposite".

csc∠A=cacsc∠A=ca

The cotangent is given by the ratio "adjacent over opposite".

cot∠A=ba