Trigonometric Ratios
"Trigon" is Greek for triangle , and "metric" is Greek for measurement. The trigonometric ratios are special measurements of a right triangle (a triangle with one angle measuring ). 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- angles.
Example:
Write expressions for the sine, cosine, and tangent of .
The length of the leg opposite is . The length of the leg adjacent to is , and the length of the hypotenuse is .
The sine of the angle is given by the ratio "opposite over hypotenuse." So,
The cosine is given by the ratio "adjacent over hypotenuse."
The tangent is given by the ratio "opposite over adjacent."
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 .
The length of the leg opposite is . The length of the leg adjacent to is , and the length of the hypotenuse is .
The secant of the angle is given by the ratio "hypotenuse over adjacent". So,
The cosecant is given by the ratio "hypotenuse over opposite".
The cotangent is given by the ratio "adjacent over opposite".