Math Sept 30.notebook
September 30, 2013
Unit 2 ­ Trigonometry Foldables ­ 4 sheets of paper
Sections: Angles in Degrees and Radians
The Unit Circle
Trig Ratios
Graphing Trig Functions
Solving Trig Equations
Proving Trig Identities
Sep 27­12:14 PM
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Math Sept 30.notebook
September 30, 2013
Objective: Demonstrate an understanding of angles in standard position, expressed in degrees and radians. Sep 29­8:59 PM
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Math Sept 30.notebook
September 30, 2013
Match the angle with its measure (in degrees). a) 700 b) 1350 c) 3000 d) ­700 e) 2200 Sep 29­9:13 PM
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Math Sept 30.notebook
September 30, 2013
Match the angle with its measure (in degrees). a) 4300 b) ­2250 c) 10200 d) ­7900 e) 5800 Sep 29­9:13 PM
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Math Sept 30.notebook
September 30, 2013
coterminal angles: angles in standard position with the same terminal arms
Sep 29­9:56 PM
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Math Sept 30.notebook
September 30, 2013
Definition: One radian is the measure of the central angle subtended in a circle by an arc equal in length to the radius of the circle. degrees
radians
one full rotation: one half rotation: one quarter rotation: one eighth rotation:
Note: Angle measures without units are considered to be in radians. Sep 29­8:59 PM
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Math Sept 30.notebook
September 30, 2013
Example: For each angle in standard position, determine one positive and one negative angle measure that is coterminal with it. a) 2700
b) ­5π/4
c) 7400
The General Form
Any given angle has an infinite number of angles coterminal with it. Angles coterminal with any angle can be expressed as: Sep 29­9:59 PM
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Math Sept 30.notebook
September 30, 2013
Example: Change each degree measure to radian measure and each radian measure to degree measure. a) 300
b) ­1200
c) 5π/4
d) 2.57
Sep 29­10:01 PM
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Math Sept 30.notebook
September 30, 2013
Sep 29­10:20 PM
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Math Sept 30.notebook
September 30, 2013
Arc Length of a Circle
a = r
Caution: This formula works for any circle, provided that is measured in radians, and a and r are both measured in the same units. Sep 29­10:23 PM
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Math Sept 30.notebook
September 30, 2013
Summary: • angles can be measured using different units, including degrees and radians
• an angle measured in one unit can be converted to the other using the relationships 1 full rotation = 3600 = 2π
• angles that are coterminal have the same initial arm and the same terminal arm
• an angle has an infinite number of coterminal angles
Sep 29­10:12 PM
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Math Sept 30.notebook
September 30, 2013
Homework
page 175­179 # 3, 4, 6, 9, 11, 12, 14, 19, C1
Push Yourself! Try #27
Sep 29­9:27 PM
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