Question

90 POINTS PLEASE HELP Describe the three main trigonometry functions, their ratios and reciprocal functions.

Answer 1

Answer and Step-by-step explanation:

There are three reciprocal trigonometric functions

making a total of six including cosine, sine, and tangent.

→The reciprocal cosine function is secant: sec(Ф)=1/cos(Ф).

→The reciprocal sine function is cosecant, csc(Ф)=1/sin(Ф).

→The reciprocal tangent function is cotangent, expressed two ways: cot(Ф)=1/tan(Ф) or cot(Ф)=cos(Ф)/sin(Ф).

We've already learned the basic trig ratios:

sin(A) = a/c

cos(B) = b/c

tan(C) = a/b

   

But there are three more ratios to think about:

→Instead of  a/c, we can consider c/a  

​→Instead of  b/c, we can consider c/b  

→Instead of  a/b, we can consider b/a  

These new ratios are the reciprocal trigonometric ratios, and we’re about to learn their names.

The cosecant (csc)

The cosecant is the reciprocal of the sine. It is the ratio of the hypotenuse to the side opposite a given angle in a right triangle.

sin(A) = opp / hyp  = a/c

csc(A) = hyp / opp = c/a

The secant (sec)

The secant is the reciprocal of the cosine. It is the ratio of the hypotenuse to the side adjacent to a given angle in a right triangle.

cos(A) = adj/hyp = b/c

sec(A) = hyp/adj = c/b  

The cotangent (cot)

The cotangent is the reciprocal of the tangent. It is the ratio of the adjacent side to the opposite side in a right triangle.

tan(A) = opp/adj = a/b

cot(A) =adj/opp = b/c