Introduction to Circular Functions

Hey Guys!

Today's class reviewed some trigonometric topics covered in Grade 11 Pre-Cal, as well as introduced Radians and examined the relationship between the value of π and angles both in Degrees and Radians. The discovery of this relationship allowed us to calculate either Radians or Degrees.

Reviewed Grade 11 topics:

TERMINOLOGY:

- Initial Side = The position at which the ray originates

- Terminal Side = The position at which the ray ends/terminates

- Reference Angle = The angle between the terminal arm and the x-axis. This value is less than 90°  
                             


OTHER:

- An unknown Angular measurement is denoted by the Greet letter theta

New Concepts: 

- Radians = A unit of angular measurement 

                   Important Note: The value of the central angle that intercepts the arc is 1 Radian when the arc of a circle is  
                                                     equal to the radius of the circle.

                                                     EQUATION:   Central angle = arc length
                                                                              1 Rotation       circumference 


- π is the approximate Radian value of 3.141592654, and correlates with the Degree value of 180°.

π = 180° = 3.141592654

- Converting between Degrees and Radians 

- Recognizing the Relationship between Pi and Degree measurements

If π = 180° then 2π = 360°
If π = 180° then π/2 = 90°
If π = 180° then 3π/2 = 270°

We can then apply the relationship between π and Degrees to Graph labelling

- In addition, we examined the correlation between the number of revolutions made and the Degree measurement, allowing us to further calculate Radians in both exact and approximate values.

- Direction of Rotation 
 
Positive = Counter-Clockwise
Negative = Clockwise

•    Counter-Clockwise rotation is denoted by a positive angular measurement

              ex.) 90° = rotation of 90° in a counter-clockwise direction of rotation
                                                        or
                     1.57 = rotation of 1.57 Radians in a counter-clockwise direction of rotation

•    Clockwise rotation is denoted by a negative angular measurement

              ex.) -90° = rotation of 90° in a clockwise direction of rotation
                                                    or
                    -1.57 = rotation of 1.57 Radians in a clockwise direction of rotation

- Co-Terminal Angles

 - These are angles which share terminal sides