what is the period of sine and cosine graphs

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what is the period of sine and cosine graphs The sine cosine secant and cosecant functions have a period of 2 2 Since the tangent and cotangent functions repeat on an interval of length their period is Figure 9 Figure 9 The six trigonometric functions are periodic

The basic sine and cosine functions have a period of 2 The function sin x is odd so its graph is symmetric about the origin The function cos x is even so its graph is symmetric about the y axis The graph of a sinusoidal function has the same general shape as a sine or cosine function The period has a relationship to the value before the This pattern is probably easiest to see if we make a table Equation Period Picture y sin 1 y s i n 1 2 2 y sin 2 y s i n 2 1 1

what is the period of sine and cosine graphs

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what is the period of sine and cosine graphs
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Math Magic With Ms Laster Graphs Of Sine And Cosine
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Cosine Graph
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The sine and cosine graphs both have range 1 1 1 1 and repeat values every 2 pi 2 called the amplitude and period However the graphs differ in other ways such as intervals of increase and decrease The following outlines properties of each graph Properties of Sine y y intercept 0 0 x x intercept n pi n where While Period of sin Cx 2pi C Period of tan Cx pi C Period of cot Cx pi C Period of tan and cot occurs twice as frequently as sin cos because tan is slope and when you travel halfway pi radians around the unit circle you encounter another point on the same line same slope

In both graphs the shape of the graph repeats after 2 which means the functions are periodic with a period of 2 A periodic function is a function for which a specific horizontal shift P results in a function equal to the original function f x P f x for all values of x in the domain of f The basic sine and cosine functions have a period of 2 The function sinx is odd so its graph is symmetric about the origin The function cosx is even so its graph is symmetric about the y axis The graph of a sinusoidal function has the same general shape as a sine or cosine function

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Identifying the Period of a Sine or Cosine Function Determine the period of the function f x sin 6 x f x sin 6 x Example 2 sin 4 x 0 5 3 amplitude A 2 period 2 B 2 4 2 phase shift 0 5 or 0 5 to the right vertical shift D 3 In words the 2 tells us it will be 2 times taller than usual so Amplitude 2 the usual period is 2 but in our case that is sped up made shorter by the 4 in 4x so Period 2

They are periodic functions with a period of 2 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 The graph of y cos x is symmetric about the y In both graphs the shape of the graph repeats after 2 which means the functions are periodic with a period of 2 A periodic function is a function for which a specific horizontal shift P results in a function equal to the original function f x P f x for all values of x in the domain of f

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what is the period of sine and cosine graphs - In both graphs the shape of the graph repeats after 2 which means the functions are periodic with a period of 2 A periodic function is a function for which a specific horizontal shift P results in a function equal to the original function f x P f x for all values of x in the domain of f