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# In mathematics, the tangent function (or tangent) is a function that defines the slope of a straight line, or line segment, at any point along it. The slope of a line is defined as the ratio of the "vertical change" to the "horizontal change" between any two distinct points on the line. The slope of a straight line is constant, and equal to its value at the point where the line is defined, but the slope of a line segment is not constant, and is usually different from the slope of the line at either end of the line segment.

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engine function. Now, in graphic, a tangent function. It's not gonna be quite like the side and casa. It's gonna look somewhat different. The first thing you're gonna start off is you're gonna identify your size tubs. Now, we're gonna go ahead and I'm gonna label these, And this time I'm gonna label these is radiance instead of degrees. However, things were still kind of the same thing. This is still remember that pi over two. It's 90 degrees. Three pi over two is to 70. So you want to start off and you wanna find those two points and your ass Tom's. And so what these are these are gonna be dotted lines, and we're gonna put the's at our 90 degrees, are in a pile or two, and we're gonna put this and our 2 70 are the three pi over two, and that's going to kind of give us an area from where our graph is gonna go. The next thing we're gonna do is we're gonna find our ex intercepts now because we're talking about tangent. We're looking at where these are going to equal zero because remember, these are the Y, over X. So we want a flower. These equal zero and the points of things equal zero are gonna be a zero pie or 180 degrees and two pi, which is 360 degrees. So those are my three x intercepts From there, we have to determine how this graph is going to go because we're not gonna put a point at the 90 degrees into 70. So instead, let's look at just a kind of a basic graph. I know we've got a graph drawn, but let's look at this really quick. Let's say we have an angle in standard position when that angle is going toward when that terminal side is going towards that 90 degrees angle, it's in quadrant one and in quadrant one, our why is positive and even if this continues on going towards 1 80 or why is still positive. So this means that my when I graph from the Z first one, I'm going to graphic going towards that 90 degrees where my wife is positive now from the from 1 80. We know that if it's going to be the 1 80 the wise positive. But even after it leaves the 1 80 going towards to 70 here, my wife becomes negative. So at this point, we can see that if it continues going, it could be positive. But if Or it can be negative and then are going to 3. 60. This is where my wife is. Negative. So my graph would look like this. So this is an example of a tangent graph. Liberty University

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##### Top Algebra 2 Educators ##### Lily A.

Johns Hopkins University ##### Alisa L.

University of Texas at Austin  ##### Heather Z.

Oregon State University