Download CCMIII Unit 6: Modeling with Trigonometric Functions

CCMIII Unit 6: Modeling with Trigonometric Functions Vocabulary
Terms
Circle
Arc Length
AA~
Radius
Chord
Diameter
Tangent
Secant
Inscribed Angles
Intercepted Arc
Central Angles (of a
circle)
Sector (Area of)
Semicircle
Circumscribed Angle
Initial Side
Definitions
All points equidistant from a given point called the
center
The distance between two points on a circle (a fraction
of the circumference)
If two pairs of corresponding angles are ≅, then the
correspondence is a similarity
A segment from the center to a point of the circle
A segment whose endpoints are on the circle
A special chord that passes through the center
A line (in the same plane) which intersects the circle in
one and only one point
A line which intersects the circle in two points
An angle whose vertex is a point on the circle and the
sides of the angle contain the end points of the arc
The arc in the interior of an angle
An angle whose vertex is the center of the circle
The interior formed by a central angle and its
intercepted arc (“pie” shape)
Arc of a circle that measures 180⁰
An angle whose vertex is a point in the exterior of the
circle and the sides of the angle intercepts the circle in 2
different arcs
Ray that remains fixed; Angle of rotation begins from
this ray
Terminal Side
Ray that rotates away from the initial side; where the
angle ends.
Positive Angle
Angle that has counterclockwise rotation
Negative Angle
Angle that has a clockwise rotation
Standard Position
When an angle has its vertex at the origin and its initial
side along the positive x-axis
Quadrantal Angle
When the terminal side of an angle in standard position
coincides with one of the axes.
Degrees
Angle measure; full rotation is 360°.
Radian
The measure of a central angle whose sides intercept an
arc that is the same length as the radius of the circle.
Two angles in standard position that have the same
terminal side.
Coterminal Angles
Reference Angles
Minor Arc
Major Arc
FORMULAS
Area of Sector
Area of Sector
Arc Length
Arc Length
Equation of a Circle
Inscribed Angle
Measure
Reference Angles
Degree/Conversion
Formulas
The angle formed between the terminal side of an angle
and the x-axis.
Arc that measures less than 180˚
Arc that measures greater than 180˚
𝑚𝑒𝑎𝑠𝑢𝑟𝑒 𝑜𝑓 𝑐𝑒𝑛𝑡𝑟𝑎𝑙 𝑎𝑛𝑔𝑙𝑒
360
𝑚𝑒𝑎𝑠𝑢𝑟𝑒 𝑜𝑓 𝑐𝑒𝑛𝑡𝑟𝑎𝑙 𝑎𝑛𝑔𝑙𝑒
2
𝑚𝑒𝑎𝑠𝑢𝑟𝑒 𝑜𝑓 𝑐𝑒𝑛𝑡𝑟𝑎𝑙 𝑎𝑛𝑔𝑙𝑒
360
𝑚𝑒𝑎𝑠𝑢𝑟𝑒 𝑜𝑓 𝑐𝑒𝑛𝑡𝑟𝑎𝑙 𝑎𝑛𝑔𝑙𝑒
2𝜋
∗ 𝜋𝑟 2 or
𝑥
360
=
𝐴
𝜋𝑟 2
if in degrees
∗ 𝑟 2 if in radians
∗ 2𝜋𝑟 or
𝑥
360
=
𝐿
2𝜋𝑟
if in degrees
∗ (2𝜋𝑟) if in radians
(𝑥 − ℎ)2 + (𝑦 − 𝑘)2 = 𝑟 2 with center (h,k) and radius r
1
(𝑚𝑒𝑎𝑠𝑢𝑟𝑒 𝑜𝑓 𝑖𝑛𝑡𝑒𝑟𝑐𝑒𝑝𝑡𝑒𝑑 𝑎𝑟𝑐)
2
a) x, when the terminal side is in Quadrant I,
b)  - x, when the terminal side is in Quadrant
II,
c) x - , when the terminal side is in Quadrant
III, and
d) 2 - x, when the terminal side is in
Quadrant IV.
180
1 radian =
degrees or about 57.3
𝜋
1 degree =
𝜋
180
radians or about 0.017 radians