5.1 Notes Day 2
August 22, 2014
5.1 Coterminal & Reference Angles
Coterminal Angles ­ angles in standard positions whose terminal sides are the same.
If α = 60°, how could I find a coterminal angle?
Equation for coterminal angles:
α ± 360k, where α is the angle between 0° & 360°
k is the number of rotations
Aug 22­5:24 PM
Examples:
Identify all coterminal angles, then find one positive and one negative coterminal angle.
1. 45
2. 225
3. 86
4. 294
Aug 22­5:26 PM
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5.1 Notes Day 2
August 22, 2014
Usefulness of coterminal angles:
Find an angle between 0 and 360 that is coterminal with each angle.
1. 775
2. ­1297
3. 595
4. ­777
Aug 22­5:29 PM
Reference Angles ­ an acute angle (< 90), that is formed by the terminal side & x­axis
*draw out the given angle
*draw a right triangle from the terminal side down to the x­axis
* reference angle is the acute angle with a vertex at the origin
Aug 22­5:30 PM
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5.1 Notes Day 2
August 22, 2014
Examples: Find the measure of the reference angle.
1. 120°
2. 225°
rules:
Quad I = α
Quad II = 180 ­ α
Quad III = α ­ 180
Quad IV = 360 ­ α
3. 312°
4. 65°
Aug 22­5:33 PM
What if the original angle is more than 360 or negative? How should we find the reference angle?
Example: ­1205°
1. Find an angle between 0° and 360° that is coterminal with the original angle
2. Use the new angle to find the reference angle
Aug 22­5:34 PM
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5.1 Notes Day 2
August 22, 2014
Find the Reference Angle
Aug 21­2:12 PM
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