1. Chapter 4.3
Trigonometry Extended: The Circular
Functions

2. Standard Position
 An angle with its vertex at the origin.
 The initial side lies along the positive
x-axis.

3. Quadrantal Angle
 When the terminal side coincides with
one of the axes.
900
00 or
1800
3600
2700

4. Acute Angle
 If the terminal side falls in the first
quadrant it is said to be an acute angle.
 Generally talking about an angle formed
in the normal way (standard position),
positive or counter clock wise.

5. Obtuse Angle
 If the terminal side falls in the second
quadrant it is said to be an obtuse angle.
 Generally talking about an angle formed
in the normal way (standard position),
positive or counter clock wise.

6. Coterminal Angles
 Two angles in standard position that
share the same terminal side.
 Angles that differ by multiples of 3600.
 Every angle has infinitely many
coterminal angles. (α + 360ko)
α – angle
k - integer

7. Reference Angle
 For any angle α , 0o < α < 360o
 The reference angle is the acute angle
formed by the terminal side and the
closest x-axis.

8. The Unit Circle
A circle with a radius of 1
It’s center is at the origin
Symmetric to the x-axis, the y-axis, and the
origin

9. Sine and Cosine
 Ifthe terminal side of an angle θ
in standard position intersects
the unit circle at P(x, y), then
cos θ = x and sin θ = y.
 Sine and cosine always range
between -1 and 1.

10. Trig Functions of an Angle in
Standard Position

11. Trig Functions of an Angle in
Standard Position