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You can write ordered pairs as ratios to determine if two sets of ordered pairs form a linear or non-linear relationship. In a table of x,y values, the ordered pairs are listed as the x value first, then the corresponding y value. Remove from the table and write as a ratio of x over y, (or y over x, if you like). In a linear relationship, all the ratios of x over y, (or y over x) are equivalent.
x = time, y = magnitude
They are proportional if a change in one of the quantities always and necessarily results in a proportional change in the other.So if you think of a simple equation, x = 2y then the quantities are proportional. If you double y then x is necessarily also doubled. If you triple y then x is also tripled. If you halve y then x is halved and so forth.However x = 2y + 1 is non proportional. This is because if, for example, you double y then x is increased but it is not exactly doubled and so the change is not in proportion. For example, in this equation, when y = 2 then x = 5. When y = 4 then x = 9. 9 is not the double of 5.
Given a unit circle (radius = 1) and a counterclockwise angle (theta) between the positive x axis, with the x-y coordinate of the point on the circle that the angle intersects, the three basic trigonometric ratios are... 1. sine (theta) is y 2. cosine (theta) is x 3. tangent (theta) is x / y
A set X is called a proper subset of a set Y if X is contained in Y but not equal to Y.