how to find sine function from graph Step 1 Examine the graph to find the y intercept This value is the vertical shift of the graph c Step 2 Determine the amplitude of the graph The amplitude of the
The general equation of a sine graph is y A sin B x D C The general equation of a cosine graph is y A cos B x D C Examples Given a transformed graph of sine or cosine determine a possible equation Show Video Lesson Trigonometry Finding An Equation From A Graph Writing Equation Of Sin And Cos Graph Examples Sketch a graph of f x 3 sin left dfrac pi 4 x dfrac pi 4 right Solution Step 1 The function is already written in general form f x 3 sin left dfrac pi 4 x dfrac pi 4 right This graph will have the shape of a sine function starting at the midline and increasing to the right
how to find sine function from graph
how to find sine function from graph
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Graphing Sine Cosine Functions With Multiple Transformations 5 2c
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Cosine Graph
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Finding features from graph Given the graph of a sinusoidal function we can analyze it to find the midline amplitude and period Consider for example the following graph A graph of a trigonometric wave on an x y coordinate plane The x and y axes scale by one The midline is at y equals five Given the graph of a sinusoidal function we can write its equation in the form y A sin B x C D using the following steps D To find D take the average of a local maximum and minimum of the sinusoid y D is the midline or the line around which the sinusoid is centered
The graph of y sin x is like a wave that forever oscillates between 1 and 1 in a shape that repeats itself every 2 units Specifically this means that the domain of sin x is all real numbers and the range is 1 1 See how we find the graph of y sin x using the unit circle definition of sin x Free online graphing calculator graph functions conics and inequalities interactively
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How To Find The Period Of A Sine Graph
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The sine is an odd function symmetric about the origin so sin theta sin theta The cosine is an even function symmetric about the y axis so cos theta cos theta These identities can be used among other purposes for helping with simplification and proving identities For a sine or cosine graph simply go from 0 to 2 on the x axis and 1 to 1 on the y axis intersecting at the origin 0 0 Both y sin x displaystyle y sin x and y cos x displaystyle y cos x repeat the same shape from negative infinity to positive infinity on the x axis you ll generally only graph a portion
Graph the following three functions y sin x space space y sin dfrac 1 2 x space space y sin dfrac 1 4 x using the following settings for the viewing window 0 leq x leq pi and 1 5 leq y leq 1 5 If possible on your graphing utility set it so that the tickmarks on the x axis are spaced at dfrac pi 2 The general equation of a sine graph is y a sin b x h k where a is the amplitude b is the period h is the horizontal shift and k is the vertical shift Related Topics How to Graph the Sine Function How to Graph the Cosine Function How to Graph Inverse of the Sine Function
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Transforming Sine And Cosine Graphs examples Solutions Worksheets
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how to find sine function from graph - Given a sinusoidal function in the form f x A sin B x C D f x A sin B x C D identify the midline amplitude period and phase shift Determine the amplitude as A A