ʕ•ᴥ•ʔ Unit Circle and Reference Angle Trigonometry Explained

Quickly master unit circle and reference angle Trigonometry. Watch more lessons like this and try our practice at https://www.studypug.com/algebra-2/trigonometry/unit-circle

What is a unit circle? Unit circle is nothing crazy. It’s just a circle with radius equal one. Unit circle just means we have a circle with radius, radius equals one. R-A-D-I-U-S, okay? It’s nothing crazy, it’s just a circle with radius equals one, and we give you a cool name, “Unit Circle”. Okay, so here it is X-axis and Y-axis. So that’s our unit circle. Let’s draw our unit circle.

So basically it’s a circle with radius, we got to draw our radius right here. The radius equal one. Okay guys? So here it is. Let me show you something pretty cool. So now guys, now from here I’m going to draw a triangle. Okay so once again, imagine you have a terminal arm right here. This is your terminal arm. How do you draw a triangle out of it? You always connect the terminal arm to X-axis. You guys see that? Okay, so now check this out. Because any point has X coordinate and Y coordinate, right?

Any point. Okay so that means what guys? That means the length right here– That means the length right here– You know what, I’m going to use another color. So the length right here is what? X right? Nothing crazy. Now let’s use another color. So the length right here will represent what? Y, right? Nothing crazy, right? For example, I’m going to give you an example. Let’s say, we have a point of three and two. That means what guys? If I draw a triangle. That means when X is three, that means what? Here, we have three. One, two, three, right? So that’s why the X coordinate is three. Y is two, that means what? Here, one, two, right? That’s why the Y coordinate is two. Right? So we’re going to ask you, “Hey, what’s the length? How long is this?” You will say, the length of this is what? Three, right? Yeah, easy as that.

We’re going to ask you what is the– We’ll use another color. Now, what is the length for the Y right here. So the length here will be what? Two, right? Length will be two. Right? Nothing crazy. So once again, for any point we have the X coordinate, right? So X coordinate means here, the length of this will just be X. Right? It’s like this, if the X coordinate here is three, the length here should be three. Right? Same thing. X here, that means the length here is X. Right? Now, same thing as here. If the Y coordinate here is Y, that means the length of this segment should be Y. Right? Just like this here as well. When the Y coordinate here is two, that means what? The length of this segment is two. Okay? Here it is, I’m going to write something really cool.

So guys, now here we have reference angle. What color should I use? Let’s use pink. Okay so we got here. Once again, reference angle is the angle between terminal arm and X axis. So this right here is– I’m sorry, the reference angle, right? Reference angle is the angle between the terminal arm and X-axis. So here we have a reference angle, I’ll say theta. Once again, reference angle is always the most important angle with your width when we talk about trigonometry. Okay, so here it is.

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