SOLUTION: Find an angle between 0 and 0 and 360 that is co-terminal with -45, give an exact value.

Algebra ->  Trigonometry-basics -> SOLUTION: Find an angle between 0 and 0 and 360 that is co-terminal with -45, give an exact value.      Log On


   

Question 596366: Find an angle between 0 and 0 and 360 that is co-terminal with -45,
give an exact value.
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
In trigonometry, angles are usually shown in what is called standard position, with a side, taken as the initial side, coinciding with the positive x-axis.
The other side is called the terminal side, and the angle is seen as a turn or sweep from the initial side to the terminal side.
Counter-clockwise angles (turns) are considered to have a positive measure, while clockwise turns have negative measures.
The measure of one whole counter-clockwise turn would be 360%5Eo.
More than one turn is allowed, so angles can have any measure, from -infinity to +infinity.
Two counterclockwise turns would be a 720%5Eo angle.
The sides of angles differing by one or more turns (like 360%5Eo and 720%5Eo angles) coincide.
Those angles are said to be co-terminal to each other.
The 1%2F8-turn clockwise, acute angle AOB has a measure of -45%5Eo.
The other (counter-clockwise, 7%2F8-turn) angle AOB has a measure of 360%5Eo-45%5Eo=315%5Eo.
It is one of an infinite number of angles coterminal with the -45%5Eo angle AOB, but the only one between 0%5Eo and 360%5Eo is the 7%2F8-turn counter-clockwise AOB measuring highlight%28315%5Eo%29.