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In fact Sine and Cosine are like good friends: they follow each other, exactly π /2 radians (90°) apart. Plot of the Tangent Function. The Tangent function has a completely different shape ... it goes between negative and positive Infinity, crossing through 0, and at every π radians (180°), as shown on this plot.
The sine and cosine functions have several distinct characteristics: They are periodic functions with a period of 2π. The domain of each function is (− ∞, ∞) and the range is [− 1, 1]. The graph of y = sin x is symmetric about the origin, because it is an odd function.
In this section, we will interpret and create graphs of sine and cosine functions. Graphing Sine and Cosine Functions. Recall that the sine and cosine functions relate real number values to the x- and y-coordinates of a point on the unit circle. So what do they look like on a graph on a coordinate plane?
Sine and Cosine Graphs. In the graph of the sine function, the x x -axis represents values of \theta θ and the y y -axis represents values of \sin \theta sinθ. For example, \sin 0=0, sin0 = 0, implying that the point (0,0) (0,0) is a point on the sine graph.
The sine and cosine functions have several distinct characteristics: They are periodic functions with a period of 2π. The domain of each function is (− ∞, ∞) and the range is [− 1, 1]. The graph of y = sin x is symmetric about the origin, because it is an odd function.
Determine amplitude, period, phase shift, and vertical shift of a sine or cosine graph from its equation. Graph variations of y=cos x and y=sin x . Determine a function formula that would have a given sinusoidal graph.
What are the graphs and important properties of the graphs of \(y = \cos(x)\) and \(y = \sin(x)\)? What are the domains of the sine and cosine functions? What are the ranges of the sine and cosine functions?