sin2piex-cos5piex
Is this a sinusoid?
No. because 2 pie x and 5 pie x are not the same/equal.?
http://www.wolframalpha.com/input/?i=plot+y%3Dsin(2*PI*x)-cos(5*PI*x)
A sine wave or sinusoid is a mathematical curve that describes a smooth repetitive oscillation. When you add/subtract two sinusoids of differing frequencies, you get a combination wave of two frequencies, the sum, and the difference. In this problem, you see the sum(7PI) and the difference(2PI) added for form a repetitive non-smooth curve.
Okay so it is not since it is a non-smooth curve not a smooth curve.
huh? surely it is smooth, as are all sums of sines and cosines.
and it's PI. not PIE! Pie is what you eat.
sin2πx-cos5πx has a period of 2
It is not a simple sine wave, but it is sinusoidal, as shown here:
http://www.wolframalpha.com/input/?i=sin2%CF%80x-cos5%CF%80x
Actually, whether or not the terms "2πx" and "5πx" are the same or equal does not determine whether the expression "sin(2πx) - cos(5πx)" represents a sinusoid.
To determine if the expression is a sinusoid, we need to check if it follows the general form of a sinusoidal function. In general, a sinusoidal function is of the form A sin(Bx + C) + D, where A, B, C, and D are constants.
In the given expression, we have "sin(2πx) - cos(5πx)". While the expression involves trigonometric functions, it does not match the general form of a sinusoidal function since it does not have the addition or subtraction of two sinusoidal terms.
Therefore, the expression "sin(2πx) - cos(5πx)" is not a sinusoid.