Section 4.3 – Unit Circle Trigonometry
1
Section 4.3
Trigonometric Functions of Angles
An angle is formed by two rays that have a common endpoint (vertex).
One ray is called
the
initial side
and the other the
terminal side
.
A terminal angle can lie in any quadrant,
on the
x
axis or
y
axis.
An angle is in
standard position
if the vertex is at the origin of the twodimensional
plane and its initial side lies along the positive
x
axis.
Positive angles
are generated by counterclockwise rotation.
Negative angles
are
generated by clockwise rotation.
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Section 4.3 – Unit Circle Trigonometry
2
The Reference Angle or Reference Number
Let
θ
be an angle in standard position.
The
reference angle
associated with
θ
is the
acute angle (with positive measure) formed by the xaxis and the terminal side of the
angle
θ
.
When radian measure is used, the reference angle is sometimes referred to as
the reference number (because a radian angle measure is a real number).
Example 1:
Draw each angle in standard position and specify the reference angle.
a.
405
o
Note:
Notice that in part a. 405
0
terminates in the same position as 45
0
.
These type of
angles are called
coterminal angles
.
Every angle has infinitely many coterminal angles.
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 Fall '08
 Staff
 Trigonometry, Angles, Euler's formula, Unit Circle Trigonometry

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