i want to ask about maths that is what is the exact meaning of sine, cosine and tan?

Question

that is the topic of trignometric in mathe matics

Answer 1

Take a right angled triangle ABC with the side BC as base & angle B = 90. Take angle C as theta. AC is the hypotenuse. AB is the opposite side to the angle theta. BC is the adjacent side to the angle theta. sin theta is taken as the ratio of the opposite side to the hypotenuse side. Cosine theta is taken as the raio of adjacent side to the hypotenuse side and tan theta is taken as the ratio of the opposite side to the adjacent side. Similarly cosecant is the reciprocal of sin, secant is the reciprocal of cosine and cot is the reciprocal of tan

Answer 2

Sine, Cosine and Tangent are trigonometric ratios.

You might recall the setup of a right triangle. There is a base (the horizontal side lying down), a perpendicular (The upright side, the vertical one) and a hypotenuse. Let us say A is the angle between the base and hypotenuse. Then,

Sin A = Perpendicular/Hypotenuse
Cos A = Base/Hypotenuse
Tan A = Sin A/Cos A = Perpendicular/Base

There are some other ratios:

Cosec A = 1/Sin A = Hypotenuse/Perpendicular
Sec A = 1/Cos A = Hypotenuse/Base
Cot A = 1/tan A = Base/Perpendicular

Cosec is the Cosecant ratio, Sec is the Secant ratio, Cot is the Cotangent ratio

Answer 3

I am sure you know what is meant by angle. It is a measure of how much you turn things with one end fixed, and is measured in terms of 360 degree for one full turn.

Now if you consider a right angle triangle, you have three sides, with a 90 degree angle at one corner and an angle less than 90 degree at the other two corners. Then the fact is that the ratio of any two given sides is fixed for any angle between the other two sides.

So for an angle x (other than the 90 degree) at any corner you have the ratio of side opposite to this angle and the hypotenus as a constant, which is called sin x and so on.

Answer 4

All of these are the trignometric ratios.
The main thing which is to be noted that these ratios imply to only RIGHT ANGLED TRIANGLES, not the other ones.

Trigonometric functions are commonly defined as ratios of two sides of a right triangle containing the angle, and can equivalently be defined as the lengths of various line segments from a unit circle.
For history of trignometric functions, go to http://en.wikipedia.org/wiki/Sine#History

Sine Ratio------
lt represents the ratio of perpendecular {of the right angled triangle} to the hyppotanouse {of the right angled triangle}

Its inverse i.e. 1/ (sin x ) is cosecant.
This implies that cosecant is the ratio of hypotanouse to the perpendecular of the right angled triangle.

Cosine Ratio-------
lt represents the ratio of base {of the right angled triangle} to the hyppotanouse {of the right angled triangle}

Its inverse i.e. 1/ (sin x ) is secant.
This implies that cosecant is the ratio of hypotanouse to the base of the right angled triangle.

Tangent Ratio-----
lt represents the ratio of perpendecular {of the right angled triangle} to the base {of the right angled triangle}

Its inverse i.e. 1/ (sin x ) is cotangent
This implies that cosecant is the ratio of base to the perpendecular of the right angled triangle.

Answer 5

Get yourself a pencil and paper. On the paper, draw a circle - any convenient size will do. Mark the centre of the circle. This is point O. From O, draw a radius to the circumference of the circle: it meets the circumference of the circle at N. From O, draw another radius to the circumference of the circle: it meets the circumference of the circle at P. From N, draw a line that meets the radius OP at point M, such that angle NMO = 90° At the centre of the circle there is an angle: angle NOP. Let's call this angle α. That's the drawing completed. Now I can answer your question. The ratio, NM/OM is defined as the tangent of angle α. We say: tan(α) = NM / OM. The ratio, NM/ON is defined as the sine of angle α. We say: sin(α) = NM / ON The ratio, OM/ON is defined as the cosine of angle α. We say: cos(α) = OM / ON.

Answer 6

There are two easy manners to grasp it.

1) by relating to a right angled triangle!

2) By relating to a circle of radius-r (that is drawn in a first quadrant of circle), which is incidentally a hypotenuse of a right angle triangle having a vertical and a horizontal distances that connects said hypotanuse)! I am explaining it further.

Said radius / hypotanuse, horizontal and vertical maintain three pair-relations when angle of radius increases in an anticlockwise direction. Angle is regarded as increasing from horizontal-line (drawn from origin 0,0 to right of origin!)

Said relations may be memorised as....

a) Hypotanuse is radius of circle

b) Angle of radius is imagined in anticlockwise direction (from horizontal) and it will complete 360 degrees(per rotation) Angle may be remembered as "alpha"

c) Memorise side opposite to alpha ('O' start of 'opposite')

d) Memorise side adjacent to alpha ('A' start of 'adjacent')

e) Memorise Hypotanuse as ('H' start of 'hypotanuse')

You will find 6 relations

O/H and H/O (Sine and cosecant) linking 'O' and 'H'

A/H and H/A (Cosine and Secant) linking 'A' and 'H' and

O/A and A/O ( Tanjant and Co- tanjant ) linking 'O' and 'A'

By a simple memory of O, A, H and 'alpha' you may learn O/H = Sine alpha, A/H= Cos alpha and O/A= tan alpha which are basic trignometric functions (numerical values) that change as angle changes!

It has meaning that...

Sine = ratio 'O/H' for any chosen angle alpha in degress

Cosine = ratio 'A/H' for any chosen angle alpha in degress

Tanjent = ratio 'O/A' for any chosen angle alpha in degress

Memorise a related figure please!


Regaeds

Answer 7

A short cut to remember sin, cos, and tan as
Remember O A OA
where O is opposite side, A is adjacent side and H is Hypotenuse.
Then sin = O /H cos = A/H and tan = O / A
The shortcut to remember these values do the following exercise.
write (-- line is drawn for showing distance as columns)
angles 0 --- 30 ---- 60 ---- 90 below that write
---------0 ------- 1 ------ 2 ------------ 3 ----------- 4
divide by 4
--------0/4 ---- 1/4 ---- 2/4 --------- 3/4 --------- 4/4
Take square root. gives the values of
-------sin 0 ----sin 30 -----sin 45 ----- sin 60 ----sin 90
-------- 0 ------ 1/2 ---- sq.rt.1/2 ---- sqrt3/2 ---- 1 and value of
-----cos 90---cos60--- cos 45------ cos 30 ----cos 0
from this you can write other relations Tan, Cosec, Sec, and Cot.

Answer 8

all sine,cosine and tan are ratios, trigonometric.
where sine is opp.side divided by hypotenuse in a right angled triangle,cosine is adjacent side by hypotenuse while tangent is opp.side by adjacent side......

Answer 9

sine, cosine and tan are just to represent angles. they do not have a specific meaning. rather they show ratio of angles.

Answer 10

Maths:-
Maths is more commonly related to sanskrit. You need to put the right thing at the right place. So I would like to tell the people who are bad in maths that : You know the answer but you dont know how to reason it.