MAT 170 CH 4 Vocab

there exists a positive number p such that f(t+p) = f(t)

A function is periodic if _____ ?

angle of elevation

An angle formed by a horizontal line and the line of sight to an object above the horizontal line is the ________?

angle of depression

If the angle is formed by a horizontal line and a line of sight to an object below the horizontal line is the ________?

periodic

Tangent and cotangent functions are _____ functions.

pi

The period of cot and tan is _____.

Tangent, secant

The trigonometric functions that are undefined when x=0 is _____ and _____.

Cosecant, cotangent

The trigonometric functions that are undefined when y=0 is _____ and _____.

Tangent, cotangent

The trigonometric functions that do not depend on the value of r are _____ and _____.

coterminal angles

Two angles with the same initial and terminal sides but possibly different rotations

90 degrees

Two positive angles are complements if their angles add up to _____.

-1 to 1

When the inverse of cosx is restricted, the domain is ____.

0 to pi

When the inverse of cosx is restricted, the range is ____.

-1 to 1

When the inverse of sinx is restricted, the domain is _____.

-pi/2 to pi/2

When the inverse of sinx is restricted, the range is _____.

negative infinity to positive infinity

When the inverse of tanx is restricted, the domain is ____.

-pi/2 to pi/2

When the inverse of tanx is restricted, the range is _____.

cosine and secant

Which trigonometric functions are even?

vertex

a common endpoint formed by two rays

ray

a line that has only one endpoint and extends forever in the opposite direction.

standard position

an angle is in _____ _____ if its vertex is at the origin and its initial side lies along the positive x-axis.

negative angle

angles that are generated by a clockwise rotation

positive angle

angles that are generated by a counter-clockwise rotation

radian measure

any central angle that is the length of the intercepted arc divided by the circle's radius.

unit circle

circle with a radius of 1 and has its center at the origin.

cot(t)

cos(t)/sin(t) = ?

1 + cot^2(t)

csc^2(t) = ?

angle

formed by two rays with a common endpoint

trigonometry

measurement of triangles

1 + tan^2(t)

sec^2(t) = ?

tan(t)

sin(t)/cos(t) = ?

radian

the measure of the central angle of a circle that intercepts an arc equal in length to the radius of the circle.

linear speed

v=s/t

angular speed

w=angle/t