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Use the form asin(bx−c)+ d a sin (b x - c) + d to find the variables used to find the amplitude, period, phase shift, and vertical shift. Find the amplitude |a| | a |. Find the period of sin(2x) sin (2 x). Tap for more steps... π π. Find the phase shift using the formula c b c b. Tap for more steps... Phase Shift: 0 0.
Here we’ll take a few minutes to work problems that involve both the amplitude and period, giving us two variables to work with when thinking about sinusoidal equations. Click image to the left or use the URL below. 1. Find the period, amplitude and frequency of y = 2cos 1 2x and sketch a graph from 0 to 2p.
The following graph shows the temperature in NellieÕs dorm room over a 24 h period. Determine the equation of this sinusoidal function. Solution Use the graph to determine the values of the parameters a, k, d, and c, and write the equation. The axis is so The equation is T (t) 5 6 cos a p 12 (t 2 17 )b 1 19. d 5 17 k 5 p 12 24 k 5 2p 24 5 2p k ...
trigonometric graphs use mini whiteboards to explore questions of the type: Give an equation to represent the function which results from: stretching f(x)=sinx in the direction of the Y axis with a scale factor of 4. reflecting f(x)=cosx in the X axis. Describe the transformation required to transform f(x)=sinx to chlaochlú go dti f(x)=-2sinx
1. A stretch parallel to the y-axis by a factor of R, the amplitude, and 2. A translation parallel to the x-axis by either α or β (depending on whether you wish to start with sin x or cos x as the original function). Consider, for example y =sin x +cosx. This can be written in the form y =Rsin()x +α,since Rsin(x +α) =R{}sin xcosα+cosxsinα
In this section, we will graph the basic sine function and the basic cosine function and then graph other sine and cosine functions using transformations. Much of what we will do in graphing these problems will be the same as earlier graphing using transformations.
Example 1 The graph shows the function y = f(x). Sketch and label the graphs of y = 2f(x) and y = –f(x). The function y = 2f(x) is a vertical stretch of y = f(x) with scale factor 2 parallel to the y-axis. The function y = −f(x) is a reflection of y = f(x) in the x-axis. Example 2 The graph shows the function y = f(x). Sketch and label the ...
