Transcript Equations - BakerMath.org

Angles & Angle Measures
1
2
3
Notation, Definitions&
Measurement of Angles,
Coterminal, Right, Complementary,
Supplementary Angles & Intro to
Radians
Practice Problems
Notation
2

Variables for angles
 Frequently
(alpha)
 b (beta)
 g (gamma)
 Q (theta)
a
Greek letters
Definitions
3

Initial side
 Point
of origin for measuring a given angle
 Typically 0˚ (360˚)

Terminal Side
 Ending
point for measuring a given angle
 Can be any size
Measurement
4

Clockwise (CW)
 Negative

Angle
Counter-Clockwise (CCW)
 Positive
Angle
Measurement (Cont.)
5

Degrees
 May
be in decimal form (72.64˚)
 May be in Degrees/Minutes/Seconds (25˚ 43’ 37”)
 Minutes
(’)
 60’ = 1˚
 Seconds ( ” )
 60” = 1’
 90˚
= 89˚ 59’ 60”
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Measurement (Cont.)
6

Radians
 Similar
to degrees
 Always measured in terms of pi (π)
 360˚/0˚
= 2π
 90˚ = π/2
 180˚ = π
 270˚ = 3 π/2
Coterminal Angles
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
Have the same initial and terminal sides
Finding Coterminal Angles
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Add multiples of 360˚
 Subtract Multiples of 360˚
Example: Find 4 coterminal angles of 60˚
60˚ + 360˚ = 420˚
60˚ + 720˚ = 780˚
60˚ – 360˚ = -300˚
60˚ – 720˚ = -660˚

Answer: 420˚, 780˚, -300˚, -660˚
Defining Angles
9

Right Angles measure 90˚
Finding Complimentary Angles
10

For degrees:
=
90˚ - Q
or
 = 89˚ 59’ 60” – Q
Example: Find the angle complementary to 73.26˚
Finding Complementary Angles
11
Example 2: Find the angle that is complementary to
25˚ 43’ 37”.
Finding Complementary Angles
12

For Radians
=
π/2 – Q
Example: Find the complementary angle of π/4 radians.

2


4
2 


4 4
2  

4


4
Finding Supplementary Angles
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
For degrees
=

180˚ - Q
For radians
=
π-Q
Converting Between Radians and
Degrees
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To Change
Multiply by
Example
Converting Decimal Degrees to
Degrees/Minutes/Seconds
15
D˚ M’ S” = D˚ +
M ˚
 
 60 
+
 S 


3600


˚
Example: Convert 19˚ 47’ 23” to decimal degrees.
Converting Radians to
Degrees/Minutes/Seconds
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
Convert radians to decimal degrees
 Non-decimal

Multiply decimal portion by 60’
 Non-decimal

portion is in degrees
portion is minutes
Multiply decimal portion by 60” & round
 Seconds
Converting Radians to
Degrees/Minutes/Seconds (Cont.)
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Example: If Q=3 radians, approximate Q in terms of
degrees/minutes/seconds.