Each rotation of OM corresponds to a certain angle.

** **

# Zero angle of rotation

** **

Skip to content
# Magnitudes of the rotation angles: zero, flat, round, right, and inverse right angles

# Zero angle of rotation

## If OM coincides with OK, then this arrangement of rays corresponds to the **zero angle**. In trigonometry, such a mutual arrangement of rays is called the **initial position**.

# Round angle of rotation

## This is a “**full rotation**” (rot) or “**revolution**” (rev) or “**complete turn**” or “**full circle**“.

# Right angle

# Straight Angle (Flat angle)

# Inverse right angle

## If OM completes three fourths of a full circle (a three quarter rotation), it results in an **inverse right angle** (**positive =270°** or **negative =–270°** depending on the direction of rotation).

# The general concept of revolutions (turns)

**A full circle** is 360°:

1 full circle = 1 rev = 1 turn = 1 rot = 360°

**A half turn** is 180°:

1/2 rev =1/2∙360°= 180°

**A quarter turn** is 90°:

1/4 rev =1/4∙360°= 90°

**An eighth turn** is 45°:

1/8 rev=1/8∙360°= 45°

**Two revolutions**:

## 2∙360°= 720°

**One and a half revolutions**:

## 360°+1/2∙360°= 540°

# Similar topics

You are here:

Each rotation of OM corresponds to a certain angle.

** **

** **

Zero angle of rotation

If terminal side OM completes such a circle and afterwards coincides with OK, this is called a full circle (turn), which corresponds to an angle of 360**°** or 2*π* rad in the positive direction, and *−360***°** (or *−2π* rad in the negative direction).

1 full circle = 1 rev = 1 turn = 1 rot = 360°

Positive full circle (Positive round angle). Revolution

** **

If OM completes one fourth of a full circle, it results in a right angle (positive = 90° or negative = –90° depending on the direction of rotation).

Positive right angle

If terminal side OM completes half a full circle, the result is a straight angle (or a flat angle).

If OM rotates counterclockwise, it forms a positive straight angle of 180°.

If OM rotates clockwise, it forms a negative straight angle of –180°.

Positive straight angle

Positive three quarter rotation (Positive inverse right angle)

1 full circle = 1 rev = 1 turn = 1 rot = 360°

1/2 rev =1/2∙360°= 180°

1/4 rev =1/4∙360°= 90°

1/8 rev=1/8∙360°= 45°

Determining the Angle of Rotation, Radius Vector

The property of subsequent rotations

Radians and Degrees. Measuring Angles in Trigonometry

Radian Measure of angles. Formula

Formula for converting degrees to radians. Formula for converting radians to degrees

Connection of the radian with other units (minutes and seconds)

MATHVOX

Go to Top
This site uses cookies to help you work more comfortably. By continuing to browse the pages of the site, you agree to the use of cookies. If you need more information, please visit the Privacy Policy page. Agree

Privacy & Cookies Policy

This website uses cookies to improve your experience while you navigate through the website. Out of these, the cookies that are categorized as necessary are stored on your browser as they are essential for the working of basic functionalities of the website. We also use third-party cookies that help us analyze and understand how you use this website. These cookies will be stored in your browser only with your consent. You also have the option to opt-out of these cookies. But opting out of some of these cookies may affect your browsing experience.

Don`t copy text!