Trig Vocab 6.1-6.6

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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


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