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y = A sin(B(x + C)) + D. amplitude is A; period is 2 π /B; phase shift is C (positive is to the left) vertical shift is D; And here is how it looks on a graph: Note that we are using radians here, not degrees, and there are 2 π radians in a full rotation.
Graph the cosine function with changes in amplitude and period. Match a sine or cosine function to its graph and vice versa. Introduction. You know how to graph the functions \ (y = \sin x\) and \ (y = \cos x\). Now you’ll learn how to graph a whole “family” of sine and cosine functions.
The amplitude of a trigonometric function is half the distance from the highest point of the curve to the bottom point of the curve: \ [ \text { (Amplitude)} = \frac { \text { (Maximum) - (minimum)} } {2}.\] For example, if we consider the graph of \ (y=\sin (x)\)
Explore math with our beautiful, free online graphing calculator. Graph functions, plot points, visualize algebraic equations, add sliders, animate graphs, and more.
12 kwi 2024 · Learning Objectives. Graph variations of sinusoidal functions \ (y=\sin ( x )\) and \ (y=\cos ( x )\). Identify properties of a sinusoidal graph: amplitude, period, vertical shift, and phase shift. Construct a sinusoidal equation from a graph or a description.
Amplitude. The " a " in the expression y = a sin x represents the amplitude of the graph. It is an indication of how much energy the wave contains. The amplitude is the distance from the "resting" position (otherwise known as the mean value or average value) of the curve.
28 maj 2021 · Example \(\PageIndex{2}\): Identifying the Amplitude of a Sine or Cosine Function. What is the amplitude of the sinusoidal function \(f(x)=−4\sin(x)\)? Is the function stretched or compressed vertically? Solution. Let’s begin by comparing the function to the simplified form \(y=A\sin(Bx)\).
