Trigonometry: Radians Standard Position Intro to Unit Circle

   

    An angle is said to be in standard position when its vertex is at the origin in the unit circle and its initial side is fixed on the positive X axis and its Terminal side is allowed to rotate around in a circle

1 radian = measure of an angle whose rays intersect on the unit circle one arc length away
    
     You can measure an angle in degrees as most people know but you can also measure an angle in radians the way of most higher level mathematicians you can convert degrees to radians and radians to degrees by following these simple steps:

1. Put the thing you are converting over 1
EX: 270 degrees/1

2. Multiply by a CCO1 (Clever Choice of 1) conversion factor 180degrees=Pi radians making sure to make the right unit cancel degrees or radians
EX 270 degrees/1 X  Pi Radians/180 degrees (Degrees Cancel)
OR:  3Pi/2 Radians X 180 degrees/Pi Radians (Pi Cancels)

3. Cancel and then solve using Pemdas

Trigonometry: The Six Functions

     Trigonometry meaning the study of triangles is basically defined as an art resulting from a mixture of Algebra and Geometry. Trigonometry is one of the most interesting types of math around and it can be used to solve many real world problems. Today we will discuss the six basic trig functions.

The six basic trig functions are listed below
Sine           Co-secant
Cosine       Secant
Tangent      Cotangent

These Functions are used to find angles and sides in triangles and solve triangles here are there definitions.
Use the triangle above for reference.
Sine= Opposite/Hypotenuse        Co-secant= reciprocal of Sine
Cosine= Adjacent/Hypotenuse    Secant=reciprocal of Cosine
Tangent= Opposite/ Adjacent       Cotangent=reciprocal of tangent

Example Question:
In Triangle ABC A=30 degrees and a=3 what is the hypotenuse?
Sin(30)= opp./hyp. = 3/x
1/2=3/x
x=6

This an example of how a trig function would be used.