This activity challenges students to analyze the graphs and functions for sine and cosine. Graph a sine or cosine function having a different amplitude and period. Sin, cos and tan graphs worksheets, questions and revision. The graphs of periodic functions display patterns that repeat themselves at regular intervals. Sketch the curve through the indicated points for each function. Pdf amplitude and period for sine and cosine functions worksheet amplitude and period for sine and cosine functions worksheet determine the amplitude and period of each function. The basic graphs of sine and cosine have a period of 2 2. Then use the amplitude of gx to find corresponding points on its graph.
The graphs of sine and cosine functions are related to the graphs of the parent functions y sin x and y cos x, which are shown below. In the factored form, the amplitude, period, and phase shift are more apparent. Determine the amplitude, period, phase shift, and vertical shift for each. It is often helpful to factor out b when such that or. Graphing sine cosine with phase shifts worksheet with. So what do they look like on a graph on a coordinate plane. The dotted lines on this graph are asymptotes lines which the function gets closer and. Graphing sine, cosine, and tangent functions classzone.
Print graphing sine and cosine transformations worksheet. Graphing sinusoidal trig functions notes 2 cosx page 6 e sin x sinx cos x cos x think of the unit circle, and where sine and cosine are positive, or picture the graphs. Displaying all worksheets related to graphing sine and cosine. Graph sine and cosine functions, as applied in example 3. I made this for a set 2 year 11 group taking the higher gcse. Between 90\degree and 90\degree, it looks like the graph on the right as you can see, it crosses the axes once at the origin, gets very big as the angle gets close to 90\degree, and similarly gets very small as the angle gets close to 90\degree. Graphing sine cosine with phase shifts worksheet with answers. The video explains how to determine the amplitude and period of sine and cosine. Plotting the points from the table and continuing along the xaxis gives the shape of the sine function.
I will identify the phase shift and vertical translation for sine and cosine functions. Changes in amplitude and period as well as phase shifts are nothing more than transformations. Solve a reallife problem involving a trigonometric function as a model. Find an equation for a sine function that has amplitude of 5, a period of 3. Find an equation for a cosine function that has amplitude of 18.
Writing trig equations from graphs worksheet doc tessshlo. Using degrees, find the amplitude and period of each function. For 19 24, use the given information to create a sine function. We can create a table of values and use them to sketch a graph. Find an equation for a sine function that has amplitude of 4, a period of 22. Graphs of sine and cosine using f x sinx or gx cosx as a guide, graph each function. Graphs of the sine and cosine function precalculus ii. Start by graphing the parent function y sin if there is no period change b. Free worksheet pdf and answer key on graphing sine, cosine,tangent with phase shifts. Amplitude and period for sine and cosine functions worksheet. Students will need to determine if a graph has been reflected and any changes that have been made to the amplitude, period, and phase shift. Trig graphs worksheet state the equations for the following graphs.
Find an equation for a cosine function that has an amplitude of 3 5, a period of 3 2 23. Assessing your students understanding of the graphs and properties of the sine and cosine functions has never been easier. Create a table listing the coordinates of the xintercepts and extrema for fx sin x for one period, 2, on the interval 0, 2. Worksheets are graphing trig functions, amplitude and period for sine and cosine functions work, 1 of 2 graphing sine cosine and tangent functions, graphing sine and cosine work 1, honors algebra 2 name, graphs of trig functions, mslc workshop series math 1149 1150 workshop graphs of. Amplitude and period for sine and cosine functions worksheet determine the amplitude and period of each function. Graphing sine and cosine functions graph the function. Find an equation for a cosine function that has amplitude of 3. The period of a function is the horizontal distance required for a complete cycle.
Graphs of trigonometric functions berkeley city college. This digital resource which can be used as an quiz, hw, or paperless assignment is designed with goo. We see sine curves in many naturally occuring phenomena, like water waves. Find an equation for a sine function that has amplitude of 4, a period of fl.
The worksheets are aimed to guide them towards their own conclusions of the effect of yacosbx and yasinbx on the amplitude and period of the graphs of sin and cos. Free worksheetpdf and answer key on graphing sine, cosine, tanegent with vertical translations, phase shifts, and change in amplitude. Find an equation for a cosine function that has amplitude of 3, a period of 270, and a yintercept of 5. A periodic function is a function whose graph repeats itself identically from left to right. The sine function notice how the sine values are positive between \0\ and \\pi\, which correspond to the values of the sine function in quadrants i and ii on the unit circle, and the sine values are negative between \\pi\ and \2.
Feb 06, 2018 how to find the amplitude, period, phase shift, and midline vertical shift of a sine cosine function duration. Solution the amplitude is a1 3 and the period is 2 b. Basic sine function periodic functions definition, period, phase shift, amplitude, vertical shift. Find an equation for a sine function that has amplitude of 4, a period of 180, and a yintercept of. The smallest such number p is called the period of f. Free worksheetpdf and answer key on graphing sine, cosine,tangent with phase shifts. It can be completed by writing the equations for the graphs, or st. When waves have more energy, they go up and down more vigorously. Amplitude and period of sine and cosine functions the amplitude of y a sin x and y a cos x represents half the distance between the maximum and minimum values of the function. How to find the amplitude, period, phase shift, and midline vertical shift of a sine cosine function duration. M110 fa17 page 17 worksheet 15 key graphing trigonometric functions 1. Answers to graphing sine and cosine 1 p 2 p3p 2 2p642 4 6. We will use this to graph the sine and cosine function function.
Recall that the sine and cosine functions relate real number values to the \x\ and \y\coordinates of a point on the unit circle. The period of a basic sine and cosine function is 2. Without graphing the function, determine its amplitude or period as requested. Graphing trig functions practice worksheet with answers students will practice graphing sine and cosine curves. State the amplitude and period for the function y 1 2 sin 4. Find an equation for a sine function that has amplitude of 4, a period of 1800, and a yintercept of 3. It so graphs the functions with different amplitudes and periods. Give the frequency, period and amplitude of each of the following functions. Page 1 of 2 832 chapter 14 trigonometric graphs, identities, and equations for a0 and b0, the graphs of yasinbxand yacosbx each have five keyxvalues on the interval 0. Up 1 graphing sine and cosine fill in the blanks and graph. Chapter 11 434 chapter table of contents 111 graph of the sine function 112 graph of the cosine function 1 amplitude,period,and phase shift 114 writing the equation of a sine or cosine graph 115 graph of the tangent function 116 graphs of the reciprocal functions 117 graphs of inverse trigonometric functions 118 sketching trigonometric graphs chapter summary. Amplitude maximum ordinate y value period length of the smallest domain interval which corresponds to a complete cycle of values of the funcuon y sin x referring to previous graphs. Graphing sine and cosine worksheets lesson worksheets.
Worksheets are graphing trig functions, graphs of sine and cosine functions, amplitude and period for sine and cosine functions work, of the sine and cosine functions, graphs of trig functions, trig graphs work, graphing sine and cosine functions, honors algebra 2 name. Solution step 1 identify the amplitude, period, horizontal shift, and vertical shift. Determine the amplitude and period of each function. Class sorting sine or cosine rule 1 pdf math geometry. Graphing sine and cosine henry county school district. Writing sine and cosine equations from graphs worksheet pdf. Y ou can use the parent graph of the sine and cosine functions and the amplitude and period to sketch graphs of y a sin k and y a cos k. Amplitude and period for sine and cosine functions worksheet author. Graphing sine and cosine worksheet with answers amplitude period. Scaffolded questions on equation, graph involving amplitude and period. Graphs and properties of the sine and cosine part 1 period and amplitude. Now, the graph of \mathbfy\tan x is very different.
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