warm up 1. what do complementary angles add to? 2. what do supplementary angles add to? 3. find a...
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WARM UP 1. What do complementary angles add to?
2. What do supplementary angles add to?
3. Find a the complementary angle and supplementary angle to 60 degrees
Math IV Lesson 19 Essential Question: What is a coterminal
angle/ How can I find coterminal angles? How can I find complements and supplements of degrees in radians?
Standard: MM4A2. Students will use the circle to define the trigonometric functions. a. Define and understand angles measured in degrees and radians, including but not limited to 0°, 30°, 45°, 60°, 90°, their multiples, and equivalences
Two angles in standard position that share the same terminal side.
Since angles differing in radian measure by multiples of 2 , p and angles differing in degree measure by 360° are equivalent,
every angle has infinitely many coterminal angles.
Coterminal Angles
Coterminal Angles
52°
Use multiples of 360° to find positive coterminal angles.
p/3 radians
Use multiples of 2p to find positive co- terminal angles
Find one positive and one negative angle that are coterminal with an angle having a measure of 7p/4.7p 4
+ 2p = 15p 4
7p 4
- 2 p
= - p4
coterminal angles- angles that have the same terminal ray
270 degrees and -90 degreesare coterminal angles
Coterminal angles
Coterminal AnglesThey have the same initial and terminal sides.
Determine 2 coterminal angles, one positive and one negative for a 60 degree angle.
60
60 + 360 = 420 degrees
60 – 360 = -300 degrees
HOW TO FIND A COTERMINAL ANGLE?
Add or subtract 360 from any degree Add or subtract 2∏ from any radian
Example- Find one positive and one negative coterminal angle for each of the following
35 degrees ∏/6
Example : Determine two co-terminal angles (one positive and one negative) for the angle 7π/6.
Example : Find the complement and supplement of the angle π/12
Let's say we have an angle β = 600 degrees
360 degrees is once aroundthen we have 270degrees left to go
This puts us in Q3
coterminal angles600 degrees240 degrees-120 degrees960 degrees
You add or subtract 360 to get a coterminal angle
Reference Angles
• A reference angle is defined as the acute angle formed by the terminal side o the given angle and the x-axis.
57°
128°
52°
reference angle
reference angle
218°
38°
reference angle331°
29°
reference angle
Find the measure of the reference angle for each angle.
5p 4
This angle is in Quadrant III so we must find the difference between it and the x-axis.
5p 4
- =p
5p 4
- 4p 4 =
p4
reference angle
- 13p 3
This angle is coterminal with 5p/3 in quad- rant IV, so we Must find the difference be- tween it and theX-axis.
2 -p 5p 3 =
6p 3
- 5p 3 =
p3
reference angle
Find the measure of the reference angle for 510°
• 510° is coterminal with 150°, which is in quadrant III, so we must find the difference between 150° and the x-axis.
• 180° - 150° = 30°
reference angle