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.

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Presentation transcript:

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

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

Angles that have the same initial and terminal side. See the examples below.

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

Complementary Angles Sum of the angles is 90  Find the complement of each angles: 40 + x = 90 x = 50 degrees No Complement!

Finding complementary angles Complementary angles add to 90 degrees or add to ∏/2 Find an angle complementary to ∏/4 Find an angle complementary to 30 degrees

Supplementary Angles Sum of the angles is 180  Find the supplement of each angles: 40 + x = 180 x = 140 degrees x = 180 x = 60 degrees

Supplementary angles Supplementary angles add to 180 degrees or 2∏ Find angles supplementary to the following 45 degrees ∏/6

Radians

Arc measure = central angle measure

Classwork / homework  Pick 5 from each section on the worksheet to solve  P266 # 31-38