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# In mathematics, the period of a periodic function is the length of its repeating pattern. The period of a periodic function is the number of full periods of the function. The period of the sine function is the number of radians through which its graph rotates. The amplitude of a periodic function is the maximum distance of the graph from the x-axis.

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##### Ahyeon H.

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Oregon State University ##### Kristen K.

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the find, the amplitude and the periods off trigonometry functions. And we're gonna use these when we're doing our transformations with the graphs of trigonometry functions. So we need to know our amplitude is and our periods and how we Father amputees If if we have a sign, our co sign, I notice in both of these we have where it says that why equals a times cosign b of the angle and why it was a cosign be of that angle. You're gonna find your amplitude in your period. Actually, the same way you're going to find your amplitude is going to be the absolute value of a and your period is gonna be 360 degrees divided by the absolute value of B. Or if you're doing radiance is gonna be two pi divided by the absolute value of big and kind of depends on how they give it to you. Which one you want to do. And now you can if they give you radiance and you're not sure you can convert it to degrees. Now if it's a tangent, so doing a and B, there is not an amplitude for a tangent problem. The period in these, though, is 180 divided by absolute value would be or pie divided by the absolute value of being. So let's look at this one. And this one's got all three, and we're gonna do why equals three sign four of the angle of cosine and tangent. So we're gonna find the amplitude and the period of both. So let's go ahead And for our son and our coasts on there. Actually, we're gonna do the son. They're not gonna be separate answers. So our amplitude is going to be the absolute value of a And so in this case, that's gonna be the absolute value of three. Because that's what comes in front of that trigonometry function. So in front of sign or Khost on its that's your A. So that means they're amplitude. Absolute value of three is three. Our period. Remember, it's gonna be either 3 60 degrees divided by absolute value of B or two pi. This one is going. We're going to do 360 degrees divided about the absolute value of four, which would be 3 60 divided by four. So the period would be 90 degrees now the tangent. Remember, Anytime you have that tangent there is no amplitude. But you do have a period and your period for this is gonna be 180 divided by the absolute value of B. So we're talking about 180 divided by four, which would be 45 degrees. So let's look at this one. Something usually you have. These is only one. You don't have all three. But let's look at one where we just have the co sign y equals negative six cosign five of our angle. So the amplitude remember is the absolute value of a which in this case is the absolute value of negative six. Thor amplitude is six. Our period is 360 degrees divided by the absolute value of B. So for this one, we have 360 the valley by five and that would give me a 72 degrees. You could also do this with radiance if you needed to do with radiance and then lastly, why equals to change in one third? Remember with amplitude. If you're talking about a tangent, there is no amplitude. But now our period, we do have in our period is going to be we're gonna do this in radiance is going to be a 180 divided by absolute value of B or pie, divided by the absolute value of be So we're gonna do radiance. So we're gonna do pie divided by absolute value of one third, which is pie divided by one third. So we would multiply by three. So this means that this would be three pie. Liberty University

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AH
##### Ahyeon H.

University of California, Berkeley ##### Boris M.

University of North Carolina at Chapel Hill ##### Heather Z.

Oregon State University ##### Kristen K.

University of Michigan - Ann Arbor