trigonometry chapter 4

a function is symmetrical with respect to the y axis it is called a blank function

EVEN

cos theta = cos(-theta) is

EVEN

when the opposite input yield an IDENTICAL output the function is

EVEN f(-x) = f(x) OPPOSITE INPUT -x equals same output (that is positive)

what is the domain of the cosecant function ?

all real numbers except at the asymptotes = to k (pie)

what is the domain for tan

all real numbers except at the asymptotes pie/2 + k(pie)

what is the domain for cot

all real numbers except at the asymptotes, k(pie)

what is the domain of sec

all real numbers except at the asymptotes, pie/2 = k (pie)

Asin(x) A changes the blank and can causes a reflection about the

amplitude x axis

Which functions are the odd functions

sin, csc tan and cot

RANGE of INVERSE =

the DOMAIN

domain of INVERSE =

the RANGE

y = sin (Bx + C) what is the horizontal shift

the argument is Bx + C =0 so x = -C/B x= -C/B is the horizontal shift

the period for the sin function is

2 pie

what is the period of the cosecant function ?

2 pie

what is the period of cos x

2 pie just like sin

find the inverse relation of 2x + 3y

2y + 3x

1/2 ( fmax -fmin) is the

AMPLITUDE

A RELATION is a correspondence between two quantities expressed as a set of ordered pairs. the set of all th FIRST coordinates is called the the coordinates in the SECOND set is called the

DOMAIN RANGE

the domain for the sin function is

(- infinity , + infinity) or all real numbers

where is the sin function 0 ?

0, pie , 2 pie ie k(pie)

what is the amplitude of cos x

1 just like sin

y = cos (x -h) h shifts the graph y = sin (x-h)

LEFT or RIGHT

AsinBx the smaller B will make the period get

LONGER

Are any of the six trigonometric functions one to one

NO

is the amplitude defined for secant

NO

does tan have an amplitude

NO only sin and cos have an amplitude

is the reverse true cos to the negative 1 ( cos) 7pie/6 = 7 pie/6

No

IF THE FUNCTION IS SYMMETRICAL WITH RESPECT TO THE ORIGIN IT IS CALLED AN BLANK FUNCTION

ODD

SIN(-theta) = - sin theta is

ODD

IF THE OPPOSITE INPUT YEILDS THE OPPOSITE OUTPUT, the function is

ODD f(-x) = -f(x)

the SMALLEST POSITIVE value of repeating p is called the

PERIOD

y = sin(Bx + C) C is called the

PHASE or PHASE ANGLE

AsinBx A and B are called

SCALING factors, the expand or contract the graph

AsinBx a larger B, the period will get

SHORTER

y =cos(x-h) + k or with sin h and k are called AND they change the blank of the graph

TRANSLATIONS POSITION

y= cos(x) + k k shifts the graph y= sin(x) +k

UP or DOWN

so y = 1/2sin(-pie x/4) will it have a reflection?

Yes, because B is less than 0 sin(-pie x/4) =-1/2sin (pied/4)! so now there is a negative in front of the sin causing a reflection

A zero is an input that results in a blank output

ZERO

the range for the sin function is

[-1,1] note the brackets this is not point! sin goes from -1 to + 1 i.e. -1 is less than or equal to y which is less than or equal to 1

what is the domain of cos x

all real numbers

what is the range for cot

all real numbers

what is the range for tan

all real numbers

what is the range of cos x

between -1 and 1 just like sin

what is cos (cos to the negative one ( 1/5)

cos(cos to the negative one) undoes each other and the answer is 1/5 same with sin ( sin to the negative 1 ) etc

EVERY function is a RELATION, but not every RELATION is a

function

Asin(x) amplitude is

lAl

AsinBx if B is less than zero first simplify using

negative identities cos(-3x) = cos(3x) sin(-3x) = -sin(3x)

are there any zeros of cosecant

no

does sec have zeros

no just like cosecant

what is the amplitude for cot

not defined

what is the amplitude of the cosecant function

not defined NO amplitude

which functions are the even functions

only cos and sec

Asin(Bx) the factor B changes the blank and can cause a reflection about the

period y axis

what is the period for tan

pie

what is the period for cot

pie just like tan, UNLIKE sin, cos, cosecant, sec which is 2 pie

what are the asymptotes for tan

pie/2 + k(pie)

where are the asymptotes for secant

pie/2 + k(pie) the same place the zeros are for cos!

what are the zeros for cot

pie/2 + kpie

where is cos x zero

pie/2 + kpie ie pie/2, 3/2pie etc UNLIKE sin

to get the inverse of a relation just

reverse the order of the coordinates in the ordered pair

what is the range of sec

same as cosecant y is less than or equal to -1 or y is greater than or equal to 1

what is the period of sec

same as sin, cos, and cosecant 2 pie

what are the asymptotes of cosecant

x = k pie the same place the zeros are for sin!

what are the asymptotes for cot

x = k(pie)

what are the zeros for tan

x=k(pie)

what is the range of cosecant

y is less than or equal to -1 or y is greater than or equal to 1

A function is PERIODIC is the blank values repeat

y values