Equations - BakerMath.org
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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”
www.themegallery.com
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
7
Have the same initial and terminal sides
Finding Coterminal Angles
8
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
13
For degrees
=
180˚ - Q
For radians
=
π-Q
Converting Between Radians and
Degrees
14
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
16
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.)
17
Example: If Q=3 radians, approximate Q in terms of
degrees/minutes/seconds.