Transcript Warm-up:

Welcome to Trigonometry!
We’ll be “Getting’ Triggy” with these concepts…
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6.1: find exact values of trigonometric functions
(5-1)
6.2: find coterminal and reference angles and to
covert between units of angle measure (5-1)
6.3: solve for missing values in right triangles
(5-4, 5-5)
6.4: use the law of sines and cosines and
corresponding area formulas (5-6)
6.5: use the ambiguous case of the law of sines
to solve problems (5-7)
6.1 find coterminal and reference
angles and to convert between
units of angle measure (5-1)
In this section we will answer…
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How are angles measured in Trig?
What are the different units of angle measure
within degree measurement?
What does it mean for angles to be co-terminal?
How can I find a reference angle?
Angles and Their Measures
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From Geometry:
In Trig
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Angles are always
placed on the
coordinate plane.
The vertex is at the
origin and one side (the
initial side) lies along
the positive x-axis.
The other side (the
terminal side) lies in a
quadrant or on another
axii.
This is called Standard
Position.
Angle Direction:
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Angles can be
measured in two
directions.
Counter-clockwise is
positive.
Clockwise is
negative.
Degree Measurement:
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One full rotation = _________________.
The circle has been cut into 360 equal
pieces.
Measure of less than a degree can be shown
2 ways:
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Decimal pieces: 55.75º
Minutes and seconds: used for maps 103º 45’ 5”
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Each degree is divided into 60 minutes.
Each minute is divided into 60 seconds.
1º = 60’ = 3600”
Example 1
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Change to minutes and seconds
16.75
Example 1
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Change to minutes and seconds
183.47
Example 3
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Change to decimal form
29 25’ 18”
Example 4
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Change to decimal form
103 12’ 42”
Translating Rotations to
Degrees
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Give the angle measure which is represented
by each rotation:
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Example 1
5.5 rotations clockwise
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Example 2
3.3 rotations counterclockwise
Coterminal Angles
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Angles in standard position which share the
same terminal side.
150º
- 210º
Finding Coterminal Angles
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Simply add or subtract 360º as many times
as you like.
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To write a statement to find EVERY angle
coterminal with a certain angle:
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Identify all the angles which are
coterminal with the given angle. Then
find one positive and one negative
coterminal angle.
Example 1 86º
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Example 2
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594º
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If each angle is in standard position,
a) State the quadrant in which the
terminal side lies
b) Determine a coterminal angle that is
between 0º and 360º.
Example 1 595º
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Example 2 -777º
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Reference Angle:
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The acute angle formed by the terminal side of
an angle in standard position and the x-axis.
The quickest route to the x-axis.
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Let’s find some!
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Homework:
 P280
#19 – 65 odd