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