MedVision ad

range of trigonometric functions (1 Viewer)

Arithela

Member
Joined
Jun 23, 2007
Messages
306
Gender
Female
HSC
2008
how do you generally find the range of trigonometric functions? (so you can sketch the graph)

eg find the range of the function y = 1 +2sin(x/2) for 0 < x < 4pi
 

lyounamu

Reborn
Joined
Oct 28, 2007
Messages
9,998
Gender
Male
HSC
N/A
Arithela said:
how do you generally find the range of trigonometric functions? (so you can sketch the graph)

eg find the range of the function y = 1 +2sin(x/2) for 0 < x < 4pi
Remember that -1<_ sin(x/2) <_1
So -2<_ 2sin(x/2) <_ 2
So -1 <_ 1+2sin(x/2) <_3

Range: -1 <_ y <_ 3
 

lolokay

Active Member
Joined
Mar 21, 2008
Messages
1,015
Gender
Undisclosed
HSC
2009
Arithela said:
how do you generally find the range of trigonometric functions? (so you can sketch the graph)

eg find the range of the function y = 1 +2sin(x/2) for 0 < x < 4pi
the range of a sin/cos function is -1 -> 1
in this example it is 1 + 2(-1 -> 1)
= -1 -> 3
 

a-n-d-r-e-w

Member
Joined
Mar 24, 2008
Messages
55
Gender
Male
HSC
2008
Arithela said:
how do you generally find the range of trigonometric functions? (so you can sketch the graph)

eg find the range of the function y = 1 +2sin(x/2) for 0 < x < 4pi
the amplitude of the graph is 2, the graph is shifted up 1, so the range would be -1<y<3, their meant to be greater/less than or equal to signs but i dont know how to do that on the computer. hope that helps
 

Arithela

Member
Joined
Jun 23, 2007
Messages
306
Gender
Female
HSC
2008
what is the range of 1 -3cos2x?

do we have to change signs because its negative?
 
L

lsam

Guest
Arithela said:
what is the range of 1 -3cos2x?

do we have to change signs because its negative?
-2 < y < 4 (where < stands for equal to or larger)
 

lolokay

Active Member
Joined
Mar 21, 2008
Messages
1,015
Gender
Undisclosed
HSC
2009
Arithela said:
what is the range of 1 -3cos2x?

do we have to change signs because its negative?
the minimum of a cos function is the negative of the maxmimum (-1 and 1 respectively), you if you change the signs you end up with the same thing anyway
 

Iruka

Member
Joined
Jan 25, 2006
Messages
544
Gender
Undisclosed
HSC
N/A
You do have to check the given domain of your function, though. It needs to go through at least one complete period to attain all of that range (which the function in your original post does.)
 

Users Who Are Viewing This Thread (Users: 0, Guests: 1)

Top