what is the period of a sine graph Midline amplitude and period are three features of sinusoidal graphs A period of a trigonometric wave A horizontal dashed line extends through the middle of the trigonometric wave and is labeled the midline
To find the period of a sine wave with equation f x sin Ax use the formula Period 2pi A If A 1 then the period of the sine wave is 2 pi If A 1 then the period will be 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
what is the period of a sine graph
what is the period of a sine graph
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How To Find The Equation Of A Sine Graph Given Two Points Tessshebaylo
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Graphing Sin Cosine W Period Change 4 Terrific Examples
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Below is the graph of a trigonometric function It intersects its midline at 3 7 5 and again at 5 9 5 1 2 3 4 5 6 7 8 9 1 2 3 4 5 6 7 8 9 10 11 y x 3 7 5 5 9 5 What is the period of the function Give an exact value units Do 4 problems Problem Graph y sin x on the interval 0 2 pi Answer The value of b is 1 so the graph has a period of 2 pi as does y sin x The value of a is 1 so the graph has an amplitude of 1 as does y sin x
Normally the period of sin x would be 2pi long Lets compare sin 4x and sin x At x 1 sin x sin 1 sin 4x sin 4 At x 2 sin x sin 2 sin 4x sin 8 As you can see in sin x x goes up by plus 1 every time 0 1 2 3 4 On the other hand sin 4x x goes up by plus 4 every time 0 4 8 12 16 If a sine graph is horizontally stretched by a factor of 3 then the general equation has b 13 b 1 3 This is because b b is the frequency and counts the number or fraction of a period that fits in a normal period of 2 2 Graphically the sine wave will make a complete cycle in 6 6
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These functions are called periodic and the period is the minimum interval it takes to capture an interval that when repeated over and over gives the complete function The periods of the basic trigonometric functions are as follows The period of the sine function is 2 This means that the value of the function is the same every 2 units Similar to other trigonometric functions the sine function is a periodic function which means that it repeats at regular intervals
The sine and cosine functions have several distinct characteristics They are periodic functions with a period of 2 2 The domain of each function is and the range is 1 1 1 1 The graph of y sin x y sin x is symmetric about the origin because it is an odd function The formula for the period of a sine cosine function is With the standard form being Since the formula becomes Simplified the period is Report an Error Example Question 2 Find The Period Of A Sine Or Cosine Function What is the period of this graph Possible Answers Correct answer Explanation
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what is the period of a sine graph - Problem Graph y sin x on the interval 0 2 pi Answer The value of b is 1 so the graph has a period of 2 pi as does y sin x The value of a is 1 so the graph has an amplitude of 1 as does y sin x