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  and angles differing in degree measure by 360° are equivalent, every angle has infinitely many coterminal angles.

Coterminal Angles 52° Use multiples of 360° to find positive coterminal angles.  /3 radians Use multiples of 2  to find positive co- terminal angles

Find one positive and one negative angle that are coterminal with an angle having a measure of 7  /4. 7  4 + 22 = 15  4 7  4 - 22 = - 44

coterminal angles- angles that have the same terminal ray 270 degrees and -90 degrees are coterminal angles

Determine 2 coterminal angles, one positive and one negative for a 60 degree angle = 420 degrees 60 – 360 = -300 degrees

H OW 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

S QUIRREL

Example : Determine two co-terminal angles (one positive and one negative) for the angle 7 π /6. Example : Find the complement and supplement of the angle π /12

More examples Find a coterminal angle for the following 3∏/2 320 degrees

Let's say we have an angle β = 600 degrees 360 degrees is once around then we have 270 degrees left to go This puts us in Q3 coterminal angles 600 degrees 240 degrees -120 degrees 960 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 218° 38° reference angle 331° 29° reference angle

Find the measure of the reference angle for each angle. 5  4 This angle is in Quadrant III so we must find the difference between it and the x-axis. 5  4 -  55 4 - 44 4 =  4 reference angle - 13  3 This angle is coterminal with 5  /3 in quad- rant IV, so we Must find the difference be- tween it and the X-axis. 2  55 3 = 66 3 - 55 3 =  3 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. 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° 180° - 150° = 30° reference angle

Radians

Arc measure = central angle measure

Classwork / homework  Practice on reference and coterminal angles