1. Angles
by M. Bourne
An angle is a measure of the amount of rotation between two line segments. The 2 line segments (or rays) are named the initial side and terminal side as shown in the diagram.
If the rotation is anti-clockwise, the angle is positive. Clockwise rotation gives a negative angle (by convention).
Examples
Anti-clockwise, positive angle.
Clockwise, negative angle.
Angles are commonly measured in degrees or radians. If you can't wait to learn about radians, see section 7. Radians.
(There is another unit for measuring angles, called gradians. The right angle is divided into 100 gradians. Gradians are used by surveyors, but not commonly used in mathematics. However, you will see a "grad" mode on most calculators.)
Standard Position of an Angle
An angle is in standard position if the initial side is the positive x-axis and the vertex is at the origin. The 2 examples given above are in standard position.
We will use `r`, the length of the hypotenuse, and the lengths x and y when defining the trigonometric ratios in the next section.
Degrees, Minutes and Seconds
The Babylonians (who lived in modern day Iraq from 5000 BC to 500 BC) used a base `60` system of numbers. From them we get the division of time, latitude & longitude and angles in multiples of `60`.
Similar to the way hours, minutes and seconds are divided, the degree is divided into 60 minutes (') and a minute is divided into 60 seconds ("). We can write this form as: DMS or ° ' ".
Exercises
Convert the following:
1) 36°23'47" to decimal degrees
2) 58.39° to DMS
Didn't find what you are looking for on this page? Try search:
Online Algebra Solver
This algebra solver can solve a wide range of math problems. (Please be patient while it loads.)
Go to: Online algebra solver
Ready for a break?
Play a math game.
(Well, not really a math game, but each game was made using math...)
The IntMath Newsletter
Sign up for the free IntMath Newsletter. Get math study tips, information, news and updates each fortnight. Join thousands of satisfied students, teachers and parents!
Share IntMath!
Short URL for this Page
Save typing! You can use this URL to reach this page:
intmath.com/angles
Trigonometry Lessons on DVD
Easy to understand trigonometry lessons on DVD. See samples before you commit.
More info: Trigonometry videos
