Trig Vocab 6.1-6.6
one degree
1/360 revolution
central angle
a positive angle whose vertex is at the center of a circle
straight angle
an angle that measures 180 degrees, or 1/2 revolution
right angle
an angle that measures 90 degrees, or 1/4 revolution
tangent function
associates with t the ratio of the y-coordinate to the x-coordinate of p and is denoted by tan(t)=y/x, if x does not equal 0
cosine function
associates with t the x-coordinate of p and is denoted by cos(t)=x
sine function
associates with t the y-coordinate of p and is denoted by sin(t)=y
reciprocal identities
csc(theta)=1/sin(theta); sec(theta)=1/cos(theta); cot(theta)=1/tan(theta)
one minute
defined as 1/60 degree
one second
defined as 1/60 minute, or equivalently, 1/3600 degree
cotangent function
defined as cot(t)=x/y, if y does not equal 0
cosecant function
defined as csc(t)=1/y, if y does not equal 0
secant function
defined as sec(t)=1/x, if x does not equal 0
angle
formed when two rays are drawn with a common vertex
six trigonometric functions of t
found by using the coordinates of the point p= (x,y) on the unit circle corresponding to the real number t
quotient identities
fundamental identities; tan(theta)=sin(theta)/cos(theta); cot(theta)=cos(theta)/sin(theta)
sinusoidal graphs
graphs of functions of the form y=Asin(bx) or y=Acos(bx)
one radian
if the radian of the circle is "r" and the length of the arc subtended by the central angle is also "r"
periodic
if there is a positive number p such that, whenever theta is in the domain of f, so is theta+p, and f(theta+p)=f(theta)
the point on the unit circle that corresponds to t
no matter what real number t is chosen, there is a unique point p on the unit circle corresponding to it
initial side
one ray of an angle; shows the rotation of an angle
terminal side
other ray of an angle
cycle
period of a graph
ray
portion of a line that starts at a point V on the line and extends indefinitely in one direction
half-line
ray
six trigonometric functions of the angle theta
sin(theta)=sin(t); cos(theta)=cos(t); tan(theta)=tan(t); csc(theta)=csc(t); sec(theta)=sec(t); cot(theta)=cot(t)
pythagorean identities
sin^2(theta)+cos^2(theta)=1; tan^2(theta)+1=sec^2(theta); cot^2(theta)+1=csc^2(theta)
(fundamental) period
smallest value such if there is a smallest such number p
amplitude
the number absolute value A; how high/low a graph goes
phase shift
the number theta/b
negative
the rotation of the angle is clockwise
positive
the rotation of the angle is counterclockwise
vertex
the starting point V of a ray
circular functions
trigonometric functions that use the unit circle in their definitions
lies in that quadrant
when an angle theta is in standard position and the terminal side lies in a quadrant
quadrantal angle
when an angle theta is in standard position and the terminal side lies on the x- or y-axis
standard position
when an angle's vertex is at the origin of a rectangular coordinate system and its initial side coincides with the positive x-axis
wrapped
when pontes travel x units on the unit circle in the counterclockwise direction to arrive at a point
