# Angles A **ray** contains one point on a line ![[Pasted image 20220520162621.png]] An **angle** is the union of two rays with a shared endpoint ![[Pasted image 20220520162631.png]] Creating an angle is a dynamic process: 1. The first step is to place a ray. This is known as the **initial side.** 2. Next, a rotation is applied using the vertex as the origin. The amount of rotation is what determines the **degree** of the angle. 3. Finally, a second ray is placed known as the **terminal side.** ![[Pasted image 20220520162731.png]] > [!info] The Theta Symbol > The greek symbol **theta**, or $\theta$ , is often used as a variable to represent a measured angle. > > This angle can be in either degrees or radians depending on its usage. --- ## Standard Position An angle is in **standard position** if its initial angle is located on the positive x-axis. --- ## Radians vs Degrees A **radian** is the measure of a central angle *(on the interior)* of a circle that intercepts an arc equal to the radius of that circle. ![[Pasted image 20220521041342.png|200]] To convert between radians and degrees: $360\degree = 2\pi \text{ radians}$ ![[radians.mp4]] ![[Pasted image 20220520163040.png|350]] --- ## Reference Angles A **reference angle** is the smallest acute angle between the x-axis and the terminal side of an angle $\theta$. ![[Pasted image 20220520162858.png|350]] --- ## Coterminal Angles Two angles are considered **==coterminal==** if: 1. They share the same **initial side**. 2. They share the same **vertex**. 3. They share the same **terminal side**. 4. They have **different measures**. ![[Pasted image 20220521040952.png|200]] --- ## Common Angle Variables (Greek Letters) *It's common to use Greek characters as variables when describing the measure of an angle.* | Letter | Name | | | ------------------- | ----- | --- | | $\theta$ | theta | | | $\varphi$ or $\phi$ | phi | φ | | $\alpha$ | alpha | | | $\beta$ | beta | | | $\gamma$ | gamma | |