The basic cosine function is bounded by -1 and 1. It is a periodic function with a period of 2*pi radians (360 degrees).
cos(0) = 1, cos(pi/2) = 0, cos(pi) = -1, cos(3pi/2) = 0, cos(pi) = 1. In between these values it forms a smooth curve. Also, it may help to understand that when the curve crosses the x-axis, its slope is 1 or -1.
It gives a good visual represtation. like in pre-calculus graphing is important because it helps to determine the domian and range of sin, cosine, and tangent waves and helps with points. but overall its easier to see and understand
It is important for beginners because the coordinates of the graphing points are measured from the origin. More expert users don't need to do so.
The functions are periodic and so, given any value (within the range) the function can take the value several times, Graphing the function can help you determine secondary points at which the function takes a given value.
A graph with points
They intercept at:no pointsone point onlytwo points.
It is because all measurements are taken from that point: it is the fixed point of reference.
Data points must be evenly spaced.
It doesn't really. Depending on the exact value of the argument, the cosine function can give both positive and negative results, for a negative argument. As to "why" the sine, or cosine, functions have certain values, just look at the function definition. Take points on a unit circle. The sine represents the y-coordinate for any point on the circle, while the cosine represents the x-coordinate for such a point. (There are also other ways to define the sine and the cosine functions.)
A "zero of a function" is a point where the dependent value (usually, Y) is zero. In the function f(x) = x2 - 2, for example, there are zeroes at -1.414 and +1.414.The zeroes of the sine function are at all integer multiples of pi, i.e. 0, pi, 2pi, 3pi, etc. The zeroes of the cosine function are at the same points plus pi/2, i.e. pi/2, 3pi/2, 5pi/2, etc.Another way to look at this is that the zeroes of sine are the even multiples of pi/2, and the zeros of cosine are the odd multiples of pi/2.
Truthfully the purpose of graphing a circle helps to show the points in a data set. If you're also going to shade, by graphing a circle you save time in functionality to figure out what and where your data sets will be.
Typically, functions are graphed on x-y coordinates. A function of x means that for every x point, there must be a single y point. You can also many properties by graphing a function, such as the minimum and maximum points, slopes and inflection points, and the inverse of the function (y values plotted on x coordinate, and x values on y coordinate).
A discrete cosine transform (DCT) expresses a sequence of finitely many data points in terms of a sum of cosine functions oscillating at different frequencies