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Radians

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Radians

What are radians? Why use them? Converting between degrees and radians.
The basic trig functions using radians.
Solving 1 stem trig equations using radians - using features of the graph and using the unit circle method.


Class Notes | Blank Notes

Ex 33.01 Radians and conversions
Ex 34.03 Solving trig Eqns with radians

Class Notes | Blank Notes
Ex 34.04 More Practice

p154 & p155

What are radians?

Quadrants in radians

 

Angles can be measured in Degrees or Radians.
One Radian is 180/π degrees, or about 57.296

A Radians is: the angle made by taking the radius and wrapping it along the edge of the circle:

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So, a Radian "cuts out" a length of a circle's circumference equal to the radius.

There are 2π radians in a full circle

In other words, if you cut up pieces of string exactly the length from the center of a circle to its edge, how many pieces would you need to go around the edge of the circle?

Answer: 2π, or about 6.28 pieces of string.

Radians Preferred by Mathematicians

Because the radian is based on the pure idea of "the radius being laid along the circumference", it gives simple and natural results to many angle-related mathematics.

So, degrees are easier to use in everyday work, but radians are much better for mathematics

java applet animation of radians & arc length http://www.mathopenref.com/arclength.html

 

Radians can replace degrees

π radians = 180
 

2π radians = 360
 

Mouse-over the degrees or radians to see the graph change

Radians are often written as fractions of pi
 

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