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

SQUIRREL

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

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 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

Radians

radians4

radians4

3

radians4

5 radians4

7

rad28.6 rad14.3

Arc measure = central angle measure

Classwork / homework

Practice on reference and coterminal angles