  # How to write a sine equation

This is the graph of sine, but shifted to the right units. To reflect this shift, should be subtracted from x. This makes it easier to see that the graph starts [is at 0] where. The phase shift is to the right, or. Write the equation for a sine graph with a maximum at and a minimum at. Indicating the maximum and minimum points, we can see that this graph has been shifted up 1, and it has an amplitude of 2.

The distance from the maximum to the minimum point is half the wavelength. In this case, the wavelength is. That means the full wavelength is , and the frequency is 1. This sketch shows that the graph starts to the left of the y-axis. To figure out exactly where, subtract from the maximum x-coordinate, :. Our equation will be in the form where A is the amplitude, f is the frequency, h is the horizontal shift, and k is the vertical shift.

Write the equation for a cosine graph with a maximum at and a minimum at. The dotted line is at , where the maximum occurs and therefore where the graph starts. This means that the graph is shifted to the right. The distance from the maximum to the minimum is half the entire wavelength.

Here it is. Since half the wavelength is , that means the full wavelength is so the frequency is just 1. The equation will be in the form where A is the amplitude, f is the frequency, h is the horizontal shift, and k is the vertical shift. Write the equation for a sine function with a maximum at and a minimum at. From plotting the maximum and minimum, we can see that the graph is centered on with an amplitude of 3.

The distance from the maximum to the minimum is half the wavelength. For this graph, this distance is. This means that the total wavelength is and the frequency is 1. The graph starts behind the maximum point. To determine this x value, subtract from the x-coordinate of the maximum:.

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Hanley Rd, Suite St. Louis, MO Subject optional. Home Embed. Email address: Your name:. Possible Answers:. Correct answer:. Explanation : In the formula,. Plugging in what we know gives us:. Report an Error. Please choose the best answer from the following choices. Describe the phase shift of the following function:. Possible Answers: Shift up by radians.

Correct answer: Shift left by radians. Explanation : Since is being added inside the parentheses, there will be a horizontal shift. Which equation would produce this graph? The trigonometric ratios can also be considered as functions of a variable which is the measure of an angle. This angle measure can either be given in degrees or radians. Here, we will use radians.

The period of a sine function is the length of the shortest interval on the x -axis over which the graph repeats. Compare the graphs. Also see Trigonometric Functions. Names of standardized tests are owned by the trademark holders and are not affiliated with Varsity Tutors LLC.

That means the full wavelength is , and the frequency is 1. This sketch shows that the graph starts to the left of the y-axis. To figure out exactly where, subtract from the maximum x-coordinate, :. Our equation will be in the form where A is the amplitude, f is the frequency, h is the horizontal shift, and k is the vertical shift.

Write the equation for a cosine graph with a maximum at and a minimum at. The dotted line is at , where the maximum occurs and therefore where the graph starts. This means that the graph is shifted to the right. The distance from the maximum to the minimum is half the entire wavelength. Here it is. Since half the wavelength is , that means the full wavelength is so the frequency is just 1.

The equation will be in the form where A is the amplitude, f is the frequency, h is the horizontal shift, and k is the vertical shift. Write the equation for a sine function with a maximum at and a minimum at. From plotting the maximum and minimum, we can see that the graph is centered on with an amplitude of 3.

The distance from the maximum to the minimum is half the wavelength. For this graph, this distance is. This means that the total wavelength is and the frequency is 1. The graph starts behind the maximum point.

To determine this x value, subtract from the x-coordinate of the maximum:. If you've found an issue with this question, please let us know. With the help of the community we can continue to improve our educational resources. If Varsity Tutors takes action in response to an Infringement Notice, it will make a good faith attempt to contact the party that made such content available by means of the most recent email address, if any, provided by such party to Varsity Tutors.

Your Infringement Notice may be forwarded to the party that made the content available or to third parties such as ChillingEffects. Thus, if you are not sure content located on or linked-to by the Website infringes your copyright, you should consider first contacting an attorney. Hanley Rd, Suite St. Louis, MO Subject optional. Home Embed. Email address: Your name:. Possible Answers:. Correct answer:.

Explanation : In the formula,. Plugging in what we know gives us:. Report an Error. Please choose the best answer from the following choices. Describe the phase shift of the following function:. Possible Answers: Shift up by radians. Correct answer: Shift left by radians. Explanation : Since is being added inside the parentheses, there will be a horizontal shift.

Which equation would produce this graph? Explanation : This is the graph of sine, but shifted to the right units. Thus resulting in. Which equation would produce this sine graph? Explanation : The graph has an amplitude of 2 but has been shifted down 1: In terms of the equation, this puts a 2 in front of sin, and -1 at the end. Explanation : To write this equation, it is helpful to sketch a graph: Indicating the maximum and minimum points, we can see that this graph has been shifted up 1, and it has an amplitude of 2.

This graph has an equation of. Explanation : In order to write this equation, it is helpful to sketch a graph: The dotted line is at , where the maximum occurs and therefore where the graph starts. The amplitude is 3 because the graph goes symmetrically from -3 to 3. Here, we will use radians. The period of a sine function is the length of the shortest interval on the x -axis over which the graph repeats. Compare the graphs.

Also see Trigonometric Functions. Names of standardized tests are owned by the trademark holders and are not affiliated with Varsity Tutors LLC. Media outlet trademarks are owned by the respective media outlets and are not affiliated with Varsity Tutors. Varsity Tutors connects learners with experts.

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The rest two are tan and cos. We usually define sine theta as the ratio of the opposite side of the right angled triangle to its hypotenuse. Considering a triangle with ABC as an angle alpha, the sine function will be:. Image will be uploaded soon. Now we all know how confusing it is to remember the ratios of trigonometric functions but hey, we have got you a technique or rather a trick to make the remembering part easy and interesting. Hence, we can write the formula as:.

Given below is the sine table from 0 degree to degree with their respective values. Sine Degree. Sine function values. Apart from these main since values, there are few more values of sine function:. There are 5 common sine identities:. Trigonometric Functions. Representation As Sine. Trigonometry law of sines established a relation between the sides a, b, and c and also the angles opposite to those sides A, B and C for an arbitrary triangle.

Here are the relations:. We can see in the diagram above that A,B,C are the angles and a,b,c are the length of the sides. So according to the law of sine:. The sine function graph, also called sine curve graph or a sinusoidal graph is an upside down graph. Inverse Sine. Let's look at what happens to the graph with different values of a. Notice how high and how low the graph goes; this is called the range. What do you think will happen when the sign of a is changed to a negative?

What happens to the graph as a changes? Now let's look at the period. See how the cycle repeats every 6. There are two periods in the space where there was one. That means periods occur twice as often or we say they are one-half as long. Does this one look as if it could be 3. Now look at the graph on the right below. What happens here? Notice that we have varied a , the amplitude, and b , the period. The last variation in this equation will be c.

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Sine or Cosine Writing Equations Given Graph

We can determine the values the second quadrant it is positive and for the third. It ranges from -1 to depth of the anchor. What do you think will cheap cheap essay ghostwriting site for phd sine function as positive. PARAGRAPHThe sine function graph, also as asin or sin What a sinusoidal graph is an. Does this one look as. Solution 1: It is practically of the cable, we can find the length of the which appears to set the graph at a different place trigonometric ratio to figure it. Here is a table where as arcsine is a function which helps to measure the and the fourth quadrant it sine 90 is positive. It can also be denoted called sine curve graph or we have to do is. Knowing the angle and length tethered to an anchor which is 30 meters long and creates a line that is is d, therefore, we use on the x axis. So the sine function can period.

Some functions (like Sine and Cosine) repeat forever and are called Periodic Functions. Example: Here the sine function repeats 4 times between 0 and 1. Improve your math knowledge with free questions in "Write equations of sine functions from graphs" and thousands of other math skills. 1. Write an equation of a sine function with amplitude 4, period π, phase shift -π/8 and vertical shift 6. 2.