# Labeled Unit Circle With Tangent

**Labeled Unit Circle With Tangent** – Hello, and welcome to this unit cycle review! In this video we will see what the unit circle is and what it is used for.

Before we get into the unit circle itself, let’s talk degrees and radians. Usually, when you measure an angle, you measure it in degrees. For example, a right angle is 90 degrees, a right angle is 180 degrees, and there is an angle for every number in between.

## Labeled Unit Circle With Tangent

But there is actually another way to measure an angle, and that is by measuring it in radians. Measuring in radians relates the angle to (pi ), so (pi ) will be in almost any angle measure if we measure in radians.

#### Tangents Of Circles Problem (example 3) (video)

Since (pi ) is the ratio of the circumference of a circle to its diameter, it makes sense to use radii more often when working with circles.

A unit circle is a circle that has a radius of one unit and is centered at the origin. This may seem quite simple and you may get excited if you think that I am going to ask you to find the district or region. With a radius of one this wouldn’t be too difficult. But today we will look at this circle through the lens of trigonometry.

Trigonometry is the study of how the sides and angles of a triangle relate to each other. Now you’re probably wondering what circles and triangles have to do with each other, and that’s a big question! One of the most common uses of trigonometry is to find the measures of an angle with two sides of a right triangle. If we look closely at our circle, we can actually find right triangles in it. Here is an example:

We know the radius is 1 and we can use SOHCAHTOA to find that the opposite is (frac) and the adjacent side is (sqrt).

### Unit Circle: Sine And Cosine Functions

An important thing to note when discussing these angle measurements is that the angles must be in standard position. Standard position simply means that the vertex of the angle is at the origin of the circle and that a ray of the angle is on the positive (x) axis. The other angle radius is placed in the angle measure formed by traveling counter-clockwise along the circle. If a corner is not in default position, it is important to set it in default position before using the points to find your trig values.

I want you to try to find some trig values yourself with the unit circle. For now we’ll put it on the screen so you can refer to it, but eventually you might want to remember it because these values come up often in math.

We can solve this by multiplying 180 degrees by the conversion factor (frac}}). This simplifies to π rad.

The coordinates of the points on the unit circle represent the cosine and sine of the angle, respectively. We will look for the coordinates where the ratio (frac=frac}). The

### Unit Circle Labeled With Quadrantal Values

The coordinates of a point on the unit circle represent the cosine. Find (frac), which is equivalent to 240° at the coordinate ((-frac, -frac})). The x-coordinate of the point is (-frac) and its cosine is (frac).

Since we are told that the value of Ɵ is in the first quadrant and we know that the

The coordinate of a point on the unit circle represents the sine, we can look for a point on the unit circle where the

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