what is the relatioship between y=cosx and y=sinx??

Question

what is the relatioship between y=cosx and y=sinx??
and what is the link between them both??
Thanks,
Diego

Answer 1

I am not quite sure what kind of answers you are looking for....

If you are talking about the relationships of both in a unit circle, for a given X, (sin x)^2 + (cos x)^2 = 1 relationship exist. In another words, if you square the result of both functions and add them together, you'll always get 1 regardless of the value.

Because of this, you can also say, the following is also true

cos(x) = +/- sqrt((1 - sin x)^2)
sin(x) = +/- sqrt((1 - cos x)^2)

In another words, if you take one of the function, square the result and subtract that amount from 1, then take a square root of that, you get the result from the other function.

There is also a co-function relationship

cos x = sin(90 degrees - x)
sin x = cos(90 degrees - x)

In another words, the results of each are 90 degrees off phase from each other.

Answer 2

If you plot the graph of each function you will see the relation graphically. If you move the graph of y = cosx pi/2 to the right it will be just the same graph of y = sinx. To move a graph to the right means subtract the same amount in variable x. So, y = cos(x-pi/2) is the same of y = sin(x)... that is the relationship:
cos(x-pi/2)=sinx

Note: the graph of y = sinx will be the same of y = cosx if you move the graph of y = sinx pi/2 to the left. To move the graph to the left means add the same amount in x, so there is another relationship: y=sin(x+pi/2) = cosx

Answer 3

Boy, there's a lot of ways you can go here, from triangle definitions to algebra.

One thing that's cool is that if you graph both functions, you'll see that cos(x) = sin(x + 90 degrees)- in other words, they're the exact same shapes, just shifted a bit.

Answer 4

Here's another relationship:

(sin x)^2 + (cos x)^2 = 1


This is the trigonometry version of the Pithagoras Theorem. If you get the principal behind this - you'll never have any problems with trigonometry.

Anyway, here's some more:
http://en.wikipedia.org/wiki/Trigonometry#Pythagorean_identities

Answer 5

Hi:

Here what I know:

1) there the same waveform or plot expect there are 90 degrees apart from one other.
here relational formula for it :


2) sin(x) = Sqr( 1-cos(x)^2)

3) cos(x)= Sqr(1-sin(x)^2)

4) Tan(x) = Sin(x)/Cos(x)

5) Sin(x/2)= Sqr((1-cos(x)/2))


6) Sin(x)= Cos(90-x)
7) Cos(x) = Sin(90-x)

Answer 6

sin(x-pi/2) = cos(x) sin(x-ninety) = cos(x) Cosine function is the sine function translated pi/2 (or ninety stages) They both have an same era, amplitude and frequency (except you adjust the function to something like 2sin(x) or cos(2x) and so on) Sine has a 0 at (0,0) and (kpi, 0) the position ok is a continuing Cosine has a y-int at (0,a million) and its zeros are at (kpi/2,0)