Vectors and imaginary Numbers
The Unit Circle
Radians + Degrees
Q: What is a radian?
A: One radian is the measure of a central angle θ that intercepts an arc s equal in length to the radius r of the circle. (r=s) Huh?
A: One radian is the measure of a central angle θ that intercepts an arc s equal in length to the radius r of the circle. (r=s) Huh?
I'm pretty sure you know what degrees are, but in case you don't, a circle is divided into 360 degrees, like it is divided into 2π radians.
To change from radians to degrees: multiply by 180/π
To change from degrees to radians: multiply by π/180
Also, circles can have negative degrees! -150 degrees = 210 degrees
To change from radians to degrees: multiply by 180/π
To change from degrees to radians: multiply by π/180
Also, circles can have negative degrees! -150 degrees = 210 degrees
The Unit Circle
The unit circle is important to trigonometry because it helps solve simple functions and is the basis for graphing the trig functions. The points around are represented by both radians and degrees.
How to find trig functions on the unit circle:
sinθ = y cscθ = 1/y
cosθ = x secθ= 1/x
tanθ = y/x cotθ = x/y
For example, to find sin 210, you would look at the y coordinate, which is -1/2.
sinθ = y cscθ = 1/y
cosθ = x secθ= 1/x
tanθ = y/x cotθ = x/y
For example, to find sin 210, you would look at the y coordinate, which is -1/2.