The xintercepts, maximum, and minimum occur at these points. You can use these points to sketch the graphs of y a sin bx and y a cos bx. C the third factor that can affect the graph of a sine or cosine curve is known as phase shift. The gray portion of the graph indicates that the basic sine curve repeats indefinitely in the positive and negative directions.
Displaying all worksheets related to sine graph word problems. 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. Graph one complete period of the given sine or cosine curve. 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. Well start by looking at an untransformed sine wave. Graphs of sine and cosine to help us graph the sine and cosine functions, we first observe that these functions repeat their values in a regular fashion. Worksheets are graphs of sine and cosine functions, 1 of 2 graphing sine cosine and tangent functions, graphs of the sine and cosine function, graphing trig functions, graphs of trig functions, amplitude and period for sine and cosine functions work, graphing sine and cosine group exploration activity, name intro to. We call this the amplitude of the curve the height of the curve above. Each one has model problems worked out step by step, practice problems, as well as challenge questions at the sheets end. In general the number c b is known as the phase shift.
Period interval divide period by 4 critical points you need 5. This introductory worksheet gives students practice graphing 8 sine and cosine curves with amplitude and vertical shifts. Now, the graph of \mathbfy\tan x is very different. Graphs of sine and cosine functions before sketching a graph, you need to know. Mar 18, 2015 lesson starts with plotting the graphs of sine, cosine and tangent functions. Trig graphs worksheet state the equations for the following graphs. Determine the vertical shift, and draw the midline. The function y 5 sin x is called a periodic functionwith a period of 2p because for every x in the domain of the sine function, sin x 5. When the period of a sine function doubles the frequency 1 doubles. Section graphs of sine and cosine functions objectives. Worksheets are unit 5 graphing trig functions applications work omega, sine cosine and tangent practice, sine cosine and tangent practice, translating trig graphs, amplitude and period for sine and cosine functions work, an overview of important topics, graphing trig functions, math 175 trigonometry work.
Determine phase shift, then translate determine the period, then graph a dashed version of the sinecosine. Solution because the graph is a transformation of the graph of y 2cos 2 3 x, the amplitude is 2 and the period is 3 by comparing the given equation to the general equation yacosbx. Moreover, the range of each function is the interval. Which of the following graphs shows the relationship between the frequency, b, and the period, p, of a sinusoidal graph. Amplitude and period for sine and cosine functions worksheet determine the amplitude and period of each function.
The dotted lines on this graph are asymptotes lines which the function gets closer and. Find an equation for a sine function that has amplitude of 4, a period of 1800, and a yintercept of 3. Amplitude and period for sine and cosine functions worksheet author. To graph y sin x, we start with the graph of y sin x and multiply the ycoordinate of each point by. Find an equation for a cosine function that has amplitude of 18. We can obtain a more complete graph of by continuing the portion shown in figure 4.
Graphing sine and cosine functions graph the function. Students should discuss the related heights on the unit. The graph of the functiony 5 sin x is its own image under the translation t 2p,0. The graph of the sine function, called a sine curve, is shown in figure 4. Precalculus name amplitude amplitude amplitude 4 cos 5x. Graphing sine and cosine fill in the blanks and graph. The dotted lines on this graph are asymptotes lines which the function gets closer. Focusing on what a particular wave will look like at least in two dimensions, this quiz and corresponding worksheet will help you gauge your knowledge of graphing sine. The graphing worksheets are randomly created and will never repeat so you have an endless supply of quality graphing worksheets to use in the classroom or at home. Lesson starts with plotting the graphs of sine, cosine and tangent functions. Find an equation for a sine function that has amplitude of 4, a period of 22.
For each equation given, find the five main points and label them on the graph. Frequency and period using your calculator, graph the curve which results from each function. Trigonometry name pd date graphing sine and cosine. Find the equation of a sine or cosine graph solutions. Then write an equation of each graph using both sine and cosine. Activity reinforces relationship between graphs of reciprocal trig functions. The sine function has this beautiful updown curve which repeats every 2. Amplitude constant that gives vertical stretch or shrink. Find an equation for a sine function that has amplitude of 4, a period of 180, and a yintercept of. It also goes on to look at translations and reflections of the trig functions.
The graphs of sine, cosine and tangent teaching resources. Apr 07, 20 i made this for a set 2 year 11 group taking the higher gcse. Cosine is just like sine, but it starts at 1 and heads down until. Each portion of the graph in an interval of 2p is onecycle of the sine function. Graphing sine and cosine group exploration activity. This has the effect of stretching the graph vertically by a factor of 2. Trig graphs worksheet richmond county school system.
Then brings in sketching a comparison of the sine and cosine functions. The following diagram shows how to find the equation of a sine graph. Amplitude and period for sine and cosine functions worksheet. The platform to get on the ride is on top of the first hill.
This willbe thelasttime we graphtwo cyclesto illustratethe phase shift. This resource explains how to generate the graphs of sine, cosine and tangent. Find an equation for a cosine function that has an amplitude of 3 5, a period of 3 2 23. Honors algebra 2 name flagstaff unified school district. Graphs include 1 sine and cosecant on the same graph 2 cosine and secant on the same graph 3 tangent 4 cotangent students match graphs, equations and domainrange cards for a set.
Graphs of transformations of sine and cosine lets graph y 2 sin x. Method for graphing sine waves helps with this by allowing you to draw the final curve on the first try. Feel free to download and enjoy these free worksheets on functions and relations. Instead of drawing the curve itself, you draw a frame or box for the curve to fit in. The range of sine and cosine is the interval 1, 1 both these graphs are considered sinusoidal graphs. In both graphs, the shape of the graph begins repeating after 2 indeed, since any coterminal angles will have the same sine and cosine values, we could conclude that sin 2 sin and cos 2 cos. Graph a sine or cosine function having a horizontal and vertical translation. Both of these functions are defined for all real numbers, since we can evaluate the sine and cosine of any angle. Graphing worksheets graphing worksheets for practice. The graphs of all sine and cosine functions are related to the graphs of.
Free worksheet pdf and answer key on grpahing sine and cosine curves. Before, getting on to solving trigonometric equations using the graphs. You used the length of the vertical leg of a triangle in the unit circle to find the related yvalue in the sine curve. Additionally, students need to identify the amplitude, vertical shift, maximum and minimum heights of each curve. Find an equation for the sine or cosine wave when finding the equation for a trig function, try to identify if it is a sine or cosine graph. Sine and cosine worksheets pdfs with answer keys on. Sine curve definition of sine curve by the free dictionary. By thinking of sine and cosine as coordinates of points on a unit. Lesson finished with an interactive plenary where students need to evaluate trigonometric values. We start with the graph of y sin x and multiply the ycoordinate of each point by 2. Draw a solid line for the first cycle of the curve, and a dotted line for the full 2. Students are also asked to write a function from a graph. The graph of the cosine function is shown in figure 4.
Worksheet 15 key graphing trigonometric functions 1. The basic sine curve is stretched and ranges between and 2, rather than between and 1. The gray portion of the graph indicates that the basic. Draw in dashed lines to show maximum or minimum values. This is a worksheet that covers graphing sine and cosine with amplitude, period, and vertical shifts. Trigonometry name pd date graphing sine and cosine practice. Find an equation for a sine function that has amplitude of 5, a period of 3. Again,we graph two cyclesto illustratethe phase shift. In canadas wonderland there is a roller coaster that is a continuous series of identical hills that are 18m high from the ground. 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.
It includes pupil worksheets used in the powerpoint in word and pdf form. To find the value of k, add the maximum and minimum values and divide by 2. Like the sine function we can track the value of the cosine function through the 4 quadrants of the unit circle as we place it on a graph. Notice that by changing the coefficient of the function, we control its scaling factor a vertical stretch or vertical shrink of the basic sine curve. A graph having an amplitude of 2 two graphs that have the same period a graph that has been compressed along the x axis a graph that has been stretched vertically two graphs that are images of each other by reflection. Then sketch the graph of the function over the interval 211 x 2tc using the key points for each function. Sine graph word problems worksheets lesson worksheets. Graphing these points and then drawing the sine curve that connects them gives us the graph of. Graphs of the sine and cosine function precalculus ii. Sin, cos and tan graphs worksheets, questions and revision. Make sure to determine all of the important informationpoints.
115 647 1415 1447 770 288 470 483 203 80 1232 936 82 86 1118 11 613 443 1462 756 893 907 6 1439 1140 1414 618 728 255 45 192 287 567 1398 276 39 1143 678 933 884 199 1394