"Trigon" is Greek for triangle , and "metric" is Greek for measurement. The ** trigonometric ratios ** are unique dimensions of a ** right triangle ** (a triangle via one angle measuring 90 ° ). Remember that the two sides of a best triangle which create the appropriate angle are called the ** legs ** , and the 3rd side (opposite the best angle) is referred to as the hypotenuse .

Tright here are 3 standard trigonometric ratios: ** sine ** , ** cosine ** , and ** tangent ** . Given a right triangle, you have the right to find the sine (or cosine, or tangent) of either of the non- 90 ° angles.

sine = lengthofthelegoppositetotheangle lengthofhypotenusage abbreviated"sin" cosine = lengthofthelegadjacenttotheangle lengthofhypotenuse abbreviated"cos" tangent = lengthofthelegoppositetotheangle lengthofthelegadjacenttotheangle abbreviated"tan"

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** Example: **

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

* *

The length of the leg opposite * ∠ A * is a . The size of the leg adjacent to ∠ A is b , and also the length of the hypotenuse is c .

The sine of the angle is provided by the ratio "oppowebsite over hypotenusage." So,

sin ∠ A = a c

The cosine is provided by the proportion "surrounding over hypotenusage."

cos ∠ A = b c

The tangent is provided by the ratio "oppowebsite over surrounding."

tan ∠ A = a b

Generations of students have actually supplied the mnemonic " ** SOHCAHTOA ** " to remember which proportion is which. ( ** S ** ine: ** O ** ppowebsite over ** H ** ypotenusage, ** C ** osine: ** A ** djacent over ** H ** ypotenusage, ** T ** angent: ** O ** ppowebsite over ** A ** djacent.)

## Other Trigonometric Ratios

The various other prevalent trigonometric ratios are:secant = lengthofhypotenusage lengthofthelegadjacenttotheangle abbreviated"sec" sec ( x ) = 1 cos ( x ) cosecant = lengthofhypotenuse lengthofthelegoppositetotheangle abbreviated"csc" csc ( x ) = 1 sin ( x ) secant = lengthofthelegadjacenttotheangle lengthofthelegoppositetotheangle abbreviated"cot" cot ( x ) = 1 tan ( x )

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** Example: **

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

* *

The size of the leg oppowebsite ∠ A is a . The length of the leg adjacent to ∠ A is b , and also the size of the hypotenusage is c .

The secant of the angle is offered by the proportion "hypotenusage over adjacent". So,