"Trigon" is Greek because that triangle , and also "metric" is Greek because that measurement. The ** trigonometric ratios ** space special dimensions of a ** best triangle ** (a triangle v one angle measure up 90 ° ). Remember that the two sides the a appropriate triangle which form the right angle are called the ** foot ** , and the 3rd side (opposite the right angle) is referred to as the hypotenuse .

There space three simple trigonometric ratios: ** sine ** , ** cosine ** , and also ** tangent ** . Offered a appropriate triangle, friend can uncover the sine (or cosine, or tangent) of either of the non- 90 ° angles.

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

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** Example: **

write expressions for the sine, cosine, and tangent the ∠ A .

* *

The length of the foot opposite * ∠ A * is a . The length of the leg nearby to ∠ A is b , and the length of the hypotenuse is c .

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

sin ∠ A = a c

The cosine is provided by the ratio "adjacent end hypotenuse."

cos ∠ A = b c

The tangent is provided by the proportion "opposite over adjacent."

tan ∠ A = a b

Generations the students have actually used the mnemonic " ** SOHCAHTOA ** " to remember which proportion is which. ( ** S ** ine: ** O ** pposite end ** H ** ypotenuse, ** C ** osine: ** A ** djacent end ** H ** ypotenuse, ** T ** angent: ** O ** pposite over ** A ** djacent.)

## various other Trigonometric Ratios

The other typical trigonometric ratios are:secant = lengthofhypotenuse 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: **

compose expressions for the secant, cosecant, and also cotangent that ∠ A .

* *

The length of the foot opposite ∠ A is a . The length of the leg nearby to ∠ A is b , and also the length of the hypotenuse is c .

The secant the the edge is provided by the ratio "hypotenuse end adjacent". So,