How do you compare in essay form a sinusoidal equation and a linear equation?

Answer 1

Because writing skills have eroded so greatly, lots of schools make all students write essays in every class, even math class, which kills me, but oh well. Here are some ideas that you will have to develop: The basic equation for a sine function is y = A*sin(x), where A is the maximum amplitude of the sine wave. If A is one, then the simplest equation for a sine function is y = sin(x). The basic equation of a line in slope-intercept format is y = mx + b, where m is the slope of the line and b is the y-intercept. If m is one and b is zero, then the simplest equation is y = x. The sine function increases in value from zero to one as x increases from zero to 90. It then decreases in value for x > 90, returning to zero when x = 180. For values of x between 180 and 270, sin(x) becomes increasingly negative, achieving a value of -1 when x = 270. For values of x greater than 270, sin(x) becomes decreasingly negative, returning to zero again when x = 360, which is the same value as when x = 0. Hence, you can say that sin(x) is periodic. For the linear function y = x, there is no periodicity. As the value of x increases, the value of y increases. A two-fold increase in the value of x produces a two-fold increase in the value of y. A ten-fold increase in x produces a ten-fold increase in y. When x is positive, y is, too. When x is negative, so is y. Perhaps you won't have to develop that much, after all.

Answer 2

A sinusoidal equation represents a periodic function that oscillates between maximum and minimum values, such as y = A sin(Bx + C) + D. A linear equation, on the other hand, represents a straight line with a constant slope, such as y = mx + b. Sinusoidal equations involve trigonometric functions and represent wave-like patterns, whereas linear equations simply represent a straight line relationship between two variables.