Measuring Angles Flashcards
What is an angle?
What letters can be used to denote angles?
What is a standard/central angle?
What are the two rays on the x and y axes?
If the angle of rotation from the initial to the terminal side is counter-clockwise then the angle is:
Positive!
If the angle of rotation from the initial to the terminal side is clockwise then the angle is:
Negative
What is a degree?
1/360th counter-clockwise rotation
There are _______ degrees in one full rotation of an angle.
360°
What is the use of degrees?
We use them to measure Angles.
What is the advantage of using degrees to measure angles?
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
What is an acute angle?
between 0 and 90° (like an alligator mouth)
What is a right angle?
a 90° angle (corner of a picture frame)
The two rays that make up a right angle are_______________
perpendicular
What is an obtuse angle?
between 90° and 180° (beach chair)
What is a straight angle?
180° (straight line)
What is a reflex angle?
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
What is a complementary angle?
Two positive angles that add up to 90°
What is a supplementary angle?
Two positive angles that add up to 180°
What are coterminal angles?
Centered/Standard angles that share the same terminal side.
What is a positive coterminal angle?
By adding 360° to 60° makes 420° angle coterminal with 60°
What is a positive coterminal angle?
An angle of 60 degrees is coterminal with an angle of –300° degrees.
How many coterminal angles are there with any given angle?
Infinite amount!
What are radians?
Another way to measure angles instead of degrees
What is the definition of a radian?
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)
What is the unit circle?
A circle with radius 1
What would be the formula and graph of 1 radian of arc length of 1 unit?
Radius = 1 unit
We go measure Arc length of 1 unit to find 1 radian
What is the use of radians?
We can measure circles as arcs and separate those same circles as proportions.
What is the circumference of a circle?
Perimeter around, all the points that are equal distance around the center.
What is the formula for the circumference of radius r of a circle?
2πr
What is the circumference of the unit 1 circle?
2π since r = 1
A 2π radian makes a __________________ if the radius is 1.
If 360° = 2π radians, 180° = _______ in a unit circle
π radians in a unit circle
How do we convert angles from rad to deg?
multiply by 180° /π rad
Convert 1 rad to degrees:
How do we convert angles from deg to rad?
Convert 150° to rad:
From memory: 0° = _______ rad
From memory: 30° = _______ rad
From memory: 45° = _______ rad
From memory: 60° = _______ rad
From memory: 90° = _______ rad
From memory: 180° = _______ rad
From memory: 270° = _______ rad
If no angle units are given always assume that the unit for degrees is _____
radians
What is the equation that links together angle θ and arc length s for a circle of any radius r.
s = rθ
What does subtended angle mean?
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.
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.
