warm up 1. what do complementary angles add to? 2. what do supplementary angles add to? 3. find a...

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