"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: **sine**, **cosine**, 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. ( **S **ine: **O **pposite over **H**ypotenuse, **C **osine: **A **djacent over **H **ypotenuse, **T **angent: **O **pposite over **A **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