section 5.1: coterminal & reference angles...section 5.1: coterminal & reference angles...
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Section 5.1: Coterminal & Reference Angles
PreCalculus
August 20, 2015
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 a whole number of rotations
Examples:
Identify all coterminal angles, then find one positive and one negative coterminal angle.
1. 45 2. 225
3. 86 4. 294
Section 5.1: Coterminal & Reference Angles
PreCalculus
August 20, 2015
Usefulness of coterminal angles:
Find an angle between 0 and 360 that is coterminal with each angle.
5. 775 6. 1297
7. 595 8. 777
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
Section 5.1: Coterminal & Reference Angles
PreCalculus
August 20, 2015
rules:
Quad I = αQuad II = 180 αQuad III = α 180Quad IV = 360 α
Examples: Find the measure of the reference angle.
9. 120° 10. 210°
11. 312° 12. 65°
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