What are the relationships between the cosine and the sine functions?

I have a question on an assignment that says ';how is the graph of y = cos(x) linked to the graph of y = sin(x)?'; and then it asks what the relationship is between the two functions.What are the relationships between the cosine and the sine functions?
They are the same function, in a someways. The difference is the location of the relative extrema along the x-axis.For cosine function, you need to think about the unit circle. At a rotation of zero radians, the cosine component (x) of the point (1,0) is 1. At a rotation of pi/2 radians, the cosine component of your image is 0. Go another pi/2 radians, you go back to 1.A sine function of the same preimage (1,0) under the same rotations will give you the values 0, then 1 then 0. In other words, it's one rotation of pi/2 ';behind'; the cosine function. So all that's keeping them from being the same function is the difference if pi/2 between their extrema. Therefore, cos(x)=sin(x+(pi/2)) OR sin(x)=cos(x-(pi/2)). I hope this helps you. xWhat are the relationships between the cosine and the sine functions?
I can't emphasize enough that cosine is NOT the opposite of sine. :)





They are the same function, in a sense. The only distinction is the location of the relative extrema along the x-axis.





For a cosine function, think about the unit circle. At a rotation of zero radians, the cosine component (x) of the point (1,0) is 1. At a rotation of pi/2 radians, the cosine component of your image is 0. Go another pi/2 radians, you go back to 1.





A sine function of the same preimage (1,0) under the same rotations will give you the values 0, then 1 then 0. In other words, it's one rotation of pi/2 ';behind'; the cosine function.





So all that's keeping them from being the same function is the difference if pi/2 between their extrema. Therefore, cos(x)=sin(x+(pi/2)) OR sin(x)=cos(x-(pi/2))
Are you by any chance doing a grade 10 IB math portfolio, because I'm stuck on the EXACT same question.





The only thing I could find that makes sense to me is that the cosine graph doesn't cross the origin, while the sine graph does. o.O
I haven't had math in awhile so don't take my word for it completely but I THINK that cosine is like the opposite of sine.