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.
<u>The cosecant (csc)</u>
The <u>cosecant</u> 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
<u>The secant (sec)</u>
The <u>secant </u>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
<u>The cotangent (cot)</u>
The <u>cotangent </u>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
