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Graphing Sine Functions

In mathematics, the sine function or sin is a trigonometric function, defined for any angle in the interval (0,2?). It tells us how much the function changes when the angle changes by. It is also known as the "sinus" function in the old German notation.

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have a sine function. Now for this one, you're gonna go through several steps and we're gonna kind of explain what they're gonna look like. And every sine function is basically gonna look the same. There's gonna be a few differences and we'll get into that when we learn about transformations. So we're going to go through this with steps, and the first step we're going to talk about is we wanna find the X intercepts all of a sudden function. So let's talk a little bit about a graph now, just to kind of review. If I have an angle that's in standard form, that terminal side, if it's gonna make a full circle, is going to cross. The X axis is going to start at zero degrees, is going to cross the X axis at 180 degrees. And then when it comes back around, it's going across the X axis again at 360 degrees because those were the three times it crosses the X axes. And of course, it would continue if it continued all those We're gonna be our main X intercepts is where X is going to be zero where X is going to equal 180 and where X is gonna equal 360 degrees. Another way of writing this. Of course, we still have zero. But another way of writing this with radiance. This is the same as 180 would be pie Radiance. And 360 would be to pa Radiance so you can label the graph either way. So let's go ahead and let's graft those three points. So on our graph, we're gonna label it, and I'm gonna let this one b 90. This is gonna be to 70 1 80. I apologize. So that backwards 1 80 to 70 and 3 60. There's other ways you can label it, but we're gonna label it that for now. So when I draw my ex intercepts, we said our ex intercepts or where X equals 01 80 and 3 60. So we're gonna draw those three points first. Then let's to look at our graph again. If I had a graph, we want to calculate the maximum and the minimum. When we talk about maximum and minimum. We're really kind of looking at our Y coordinates. What is the highest Y coordinate and the highest low coordinate. Well, when my graph goes up and it hits that 90 degrees, that is the highest. My terminal side will be whatever point. And this is where why equals what? And that's at 90 degrees. So that means that one point for our maximum, that would be point. That would be 90 degrees or and one. So if I graft that point at 90 degrees, we're gonna eat you and obey 114 just for this one. So we're gonna also graph the point 90 in positive one for our minimum. It's going to kind of work the same way it's gonna come around. And the lowest was when it's gonna be a to 70 and that is when we're gonna have that negative one on the unit circle. So that means or why would be negative one, which would be to 70 negative one. So now that I've got my point strong, I can draw my graph and it's gonna kind of local something similar to this, and it would just kind of keep going through that pattern. And that is the graph of a sine function

Liberty University
Algebra 2

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