Chapter Four Section One

 

 

 

Radian and Degree Measuremen

 

 

 

 Trigonometry is the "measurement of angles."

 

 

Angle in standard position:

 

 

Positive angles are measured counterclockwise from the initial side.

 ex) 130°

 

 

Negative angles are measured clockwise from the initial side.

ex) -300°

 

 

 Radian

• the measurement of an angle that intercepts an arc... the radius of a circle.

= 180° 2 = 360° /2 = 90° /4 = 45° /6 = 30° /3 = 60°

 

 

Unit Circle

 

 

 

What is a Unit Circle?  A circle with a radius of one and it also has a really technical definition but all you need to know is how to use it and apply it.

 

 

 

 

 

 

 

ex) Which quadrants are these in?

     a. 5/12   QI          b. 7/4   QIV          c. -7/10   QIII

 

 

Coterminal angles are... angles with the same terminal side but different measurements.

 

                           Θ ± 360° or Θ ± 2

 

ex) Find one positive angle and one negative angle coterminal with /6

         Θ ± 2

/6 + 2 = /6 + 12/6 = 13/6

/6 - 2 = /6 - 12/6 = -11/6

 

 

Complementary angles are... two positive angles whose sum is 90°, /2

Supplementary angles are... two positive angles whose sum is 180°,

 

ex) Find the complementary and supplementary angles of 2/5

C: /2 - 2/5 = 5/10 - 4/10 = /10

S: - 2/5 = 3/5

 

 

 

Conversions

D → R : Θ · /180°

R → D : Θ · 180°/

 

ex) Convert.

   a. 135°                                                   b. 2

   135° · /180° = 135/180 = 3/4                     2 · 180°/ = 360°/ = 114.59°