what does sine, cosine,tangent,cosecant,secant,cotantgent mean?

Question

WHAT IS THE DEFINITION?

Answer 1

Sine is the ratio of the opposite leg of a triangle to the hypotenuese for a given angle of a right triangle

Cosine is the ratio of the adjacent leg of a triangle to the hypotenuese for a given angle of a right triangle

Tangent is the ratio of the opposite leg of a triangle to the adjacent leg of a triangle for a given angle of a right triangle

Here's some more identities: http://www.sosmath.com/trig/Trig5/trig5/trig5.html

Answer 2

sin is defined as follows:
For any complex number z, sin z =(1/2i)(exp(iz)-exp(-iz)).
Here i^2 = -1, exp(x) is e^x. When the series expansion for exp(x) is substituted then we get sin z = z - z^3/3! + z^5/5! ...
sin is actually a function a function from R to R. To make it a bijection we consider the strips [0,2*pi*i) and [-1,1]. In this we also get the inverse sine function.
Similarly cos z =(1/2)(exp(iz)+exp(-iz)). Once we have sin and cos we also have the other trigonometric functions tan, cosecant etc defined by tan z = sin z/cos z, cosecant z = 1/sin z and so on. Plz note that pts at which the function achieves k/0 form are excluded.
The definition that sin z = perp / hypo is not incorrect but to correctly define it one must first formally define the term angle in strict mathematical terms. Even then the definition is incomplete since it only defines sin for angles from 0 to 90. To complete it one must take recourse to identities such as sin (90 + x) = cos x etc. By an elementary theory of differential equations and some calculus it can be shown that the two definitions are equivalent.

Answer 3

Hi :

Their names for the ratios of a right triangle for it relationship of one side of the right triangle to the other side of it :


sine (Thea) = opposite side divided by the hypotenuse or
sine (Thea) = O / H

Cosine ( Thea) = Adjutant side divided by the hypotenuse or
Cosine (Thea) = A / H

Tangent ( Thea) = Opposite side divided by Adjutant side or
Tangent ( Thea) = O / A

Secant is the reverse of the Sine ratio or H / O { meaning hypotenuse divided by the opposite side }

Co-secant is the Reverse of the Cosine Ratio or H / A { meaning hypotenuse divided by adjutant side }

Cotangent is the reverse of the Tangent Ratio or A / D { meaning the Adjutant side is divided by the opposite side }


And the best way I remember those ratios is by the following saying

Oscar Had A Heap Of Apples

Take the group the letters in twos like so O H ,A H ,O A add the Division sign In between them like so and sine ,Cosine and Tangent with eqaul sign for the three group of letters like so:

sine = O / H , cosine = A / H and Tangent = O / A

The Secant,Co-Secant , Cotangent is the Reverse of the following ratios

There you go

Hope this helps you

Answer 4

This Site Might Help You.

RE:
what does sine, cosine,tangent,cosecant,secant,cotantgent mean?
WHAT IS THE DEFINITION?

Answer 5

For a right-angled triangle,

Sine of an angle is given by: the length of the side opposite to the angle divided by the length of the hypotenuse.

cosine= length of adjacent side divided by hypotenuse.
tangent= length of opp. side divided by length of adjacent side.
cosecant= 1 divided by sine of angle ( 1/sin)
secant= 1 divided by cosine of angle (1/cos)
cot= 1 divide by tangent of angle. (1/tan)

Answer 6

in a right triangle,if A is the acute angle,then
sin A =side opposite to -----------------------------
hypotenuse
cosine A=side adjacent to --------------------------
hypotenuse
tangent A=sin A
---------
cosine A
whereas cosecant A,secant Aand Cotangent A are the reciprocals of sinA,cosineAand tangentA RESPECTIVELY

Answer 7

sine = opposite / hypoentuse used to calculate the length of the side or angle for a triangle which is not a right angle (opposite side given, an angle and a side is given or two sides are)

cosine = adjacent / hypoentuse used to measure the length of the side or angle for a triangle which is not a right angle (only an angle given)

tangent = opposite / adjacent used to measure an angle of a right angle.

Answer 8

Yeah you kinda got the concept, staring / making eye contact with a girl doesn't mean the guy likes her. In MY perspective, it can mean three things: 1. The guy is comfortable talking to the girl, and is comfortable with her presence around (just friends). I plenty of friends that are girls and I always make eye contact when I talk to them, it's just casual u kno? 2. The guy wants to meet the girl / is interested in her (acquaintance). Either that, or... the girl is weird-looking or ugly lol. But still, guys wouldn't stare at a girl that long if she's like that. 3. The guy likes the girl. He doesn't know how to express his feelings, but wishes he could find a way to do so. I would tell you straight up how to tell which one of these views does a guy mean when he makes eye contact or stares, but I don't think I can. You should just.. kinda sense it. Good luck, you'll be more familiar with it along the way haha. Hope this helped ;)

Answer 9

All of them are functions of an angle!!
sin = opposite/hypotenuse
cos= adjacent/hypotenuse
tan= sin/cos
sec = 1/cos
cosec = 1/sin
cotan = 1/tan

Answer 10

Sine is the ratio of the opposite leg of a triangle to the hypotenuese for a given angle of a right triangle

Cosine is the ratio of the adjacent leg of a triangle to the hypotenuese for a given angle of a right triangle

Tangent is the ratio of the opposite leg of a triangle to the adjacent leg of a triangle for a given angle of a right triangle