Measuring Angles

Question 1

What is an angle?

Answer 1

Question 2

What letters can be used to denote angles?

Answer 2

Question 3

What is a standard/central angle?

Answer 3

Question 4

What are the two rays on the x and y axes?

Answer 4

Question 5

If the angle of rotation from the initial to the terminal side is counter-clockwise then the angle is:

Answer 5

Positive!

Question 6

If the angle of rotation from the initial to the terminal side is clockwise then the angle is:

Answer 6

Negative

Question 7

What is a degree?

Answer 7

1/360th counter-clockwise rotation

Question 8

There are _______ degrees in one full rotation of an angle.

Answer 8

360°

Question 9

What is the use of degrees?

Answer 9

We use them to measure Angles.

Question 10

What is the advantage of using degrees to measure angles?

Answer 10

the number 360° has many factors such as:
1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, 180 and 360

Question 11

What is an acute angle?

Answer 11

between 0 and 90° (like an alligator mouth)

Question 12

What is a right angle?

Answer 12

a 90° angle (corner of a picture frame)

Question 13

The two rays that make up a right angle are_______________

Answer 13

perpendicular

Question 14

What is an obtuse angle?

Answer 14

between 90° and 180° (beach chair)

Question 15

What is a straight angle?

Answer 15

180° (straight line)

Question 16

What is a reflex angle?

Answer 16

A reflex angle has a measure of more than 180°. Basically, a reflex angle is just the other side of an ordinary angle. For example, consider one of the angles in a triangle. Picture the large angle on the outside of the triangle that wraps around the corner — that’s what a reflex angle i

Question 17

What is a complementary angle?

Answer 17

Two positive angles that add up to 90°

Question 18

What is a supplementary angle?

Answer 18

Two positive angles that add up to 180°

Question 19

What are coterminal angles?

Answer 19

Centered/Standard angles that share the same terminal side.

Question 20

What is a positive coterminal angle?

Answer 20

By adding 360° to 60° makes 420° angle coterminal with 60°

Question 21

What is a positive coterminal angle?

Answer 21

An angle of 60 degrees is coterminal with an angle of –300° degrees.

Question 22

How many coterminal angles are there with any given angle?

Answer 22

Infinite amount!

Question 23

What are radians?

Answer 23

Another way to measure angles instead of degrees

Question 24

What is the definition of a radian?

Answer 24

An angle whose corresponding arc in a circle is equal to the radius of the circle.

(Find the radius, then measure an arc length of that amount will give us one radian)

Question 25

What is the unit circle?

Answer 25

A circle with radius 1

Question 26

What would be the formula and graph of 1 radian of arc length of 1 unit?

Answer 26

Radius = 1 unit We go measure Arc length of 1 unit to find 1 radian

Question 27

What is the use of radians?

Answer 27

We can measure circles as arcs and separate those same circles as proportions.

Question 28

What is the circumference of a circle?

Answer 28

Perimeter around, all the points that are equal distance around the center.

Question 29

What is the formula for the circumference of radius r of a circle?

Answer 29

2πr

Question 30

What is the circumference of the unit 1 circle?

Answer 30

2π since r = 1

Question 31

A 2π radian makes a __________________ if the radius is 1.

Answer 31

Question 32

If 360° = 2π radians, 180° = _______ in a unit circle

Answer 32

π radians in a unit circle

Question 33

How do we convert angles from rad to deg?

Answer 33

multiply by 180° /π rad

Question 34

Convert 1 rad to degrees:

Answer 34

Question 35

How do we convert angles from deg to rad?

Answer 35

Question 36

Convert 150° to rad:

Answer 36

Question 37

From memory: 0° = _______ rad

Answer 37

Question 38

From memory: 30° = _______ rad

Answer 38

Question 39

From memory: 45° = _______ rad

Answer 39

Question 40

From memory: 60° = _______ rad

Answer 40

Question 41

From memory: 90° = _______ rad

Answer 41

Question 42

From memory: 180° = _______ rad

Answer 42

Question 43

From memory: 270° = _______ rad

Answer 43

Question 44

If no angle units are given always assume that the unit for degrees is _____

Answer 44

radians

Question 45

What is the equation that links together angle θ and arc length s for a circle of any radius r.

Answer 45

s = rθ

Question 46

What does subtended angle mean?

Answer 46

Question 47

Suppose that θ = 150° is the center angle of the circle of radius 1. What would the corresponding arc length be? Convert deg to rad, plug in, and find the arc length.

Answer 47

Question 48

Suppose that θ = 150° is the center angle of the circle of radius 2. What would the corresponding arc length be? Convert deg to rad, plug in, and find the arc length.

Answer 48