what are the properties of cosines?

Answer 1

Cosine: Properties
(Math | Algebra | Functions | Properties)



Cosine: Properties
The cosine function has a number of properties that result from it being periodic and even. Most of these should not be memorized by the reader; yet, the reader should be able to instantly derive them from an understanding of the function's characteristics.

The cosine function is periodic with a period of 2p, which implies that


cos(q) = cos(q + 2p)
or more generally,

cos(q) = cos(q + 2pk), k Î integers
The function is even; therefore,


cos(-q) = cos(q)
Formula:


cos(x + y) = cos(x)cos(y) - sin(x)sin(y)
It is then easily derived that

cos(x - y) = cos(x)cos(y) + sin(x)sin(y)
Or more generally,

cos(x ± y) = cos(x)cos(y) ± sin(x)sin(y)
From the above we can easily derive that


cos(2x) = cos2(x) - sin2(x)
(The cos2(x) is alternate notation for (cos(x))2.)
By observing the graphs of sine and cosine, we can express the cosine function in terms of sine:


cos(x) = sin(x - p/2)
The pythagorean identity gives an alternate expression for cosine in terms of sine


cos2(x) = 1 - sin2(x)
The Law of Cosines relates all three sides and one of the angles of an arbitrary (not necessarily right) triangle:

c2 = a2 + b2 - 2ab cos(C).
where A, B, and C are the angles opposite sides a, b, and c respectively. It can be thought of as a generalized form of the pythagorean theorem.

Answer 2

the undeniable fact that cos(x-ninety) is unusual is beside the point. with the aid of fact cosine is an outstanding function: cos(x-ninety) = cos( -(x-ninety) ) = cos(ninety-x) you may plug in the different extensive type as a replace of ninety, and it works out the comparable way. assume we decide for 30 ranges as a replace of ninety ranges: cos(x-30) = cos( -(x-30) ) = cos(30-x) cos(30-x) is neither unusual nor even, yet that doesn't count, with the aid of fact all that concerns right that is that cosine is an outstanding function.

Answer 3

the opposite of sines

Answer 4

what is that?