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Learn how to find and interpret the amplitude, period, phase shift and frequency of periodic functions like sine and cosine. See examples, graphs and animations of different functions and their properties.
Learn how to use the periodicity identities of trigonometric functions to find their values at any angle. The period of cosine is 2pi, which means cosine(x) = cosine(x+2pi) for all x.
A period of a function is when the function has a specific horizontal shift, P, which results in a function equal to the original function, i.e., f (x+P) = f (x) for all values of x within the domain of f. The period of the cosine function is 2π.
1 lut 2024 · Learn the formula and graphical method to calculate the period of any cosine function, which is the interval over which the function repeats itself. The period depends on the coefficient of the variable inside the cosine function, not on the amplitude or phase shift.
Notation. Conventionally, an abbreviation of each trigonometric function's name is used as its symbol in formulas. Today, the most common versions of these abbreviations are "sin" for sine, "cos" for cosine, "tan" or "tg" for tangent, "sec" for secant, "csc" or "cosec" for cosecant, and "cot" or "ctg" for cotangent.
Given any function of the form \(y=a \sin b x\) or \(y=a \cos b x\), you know how to find the amplitude and period and how to use this information to graph the functions. Given a graph of a sine or cosine function, you also can determine the amplitude and period of the function.
Learn how to define and use cosine, one of the six fundamental trigonometric functions. Find cosine values for common angles, use a calculator, or reference the unit circle.
