range of trigonometric functions (1 Viewer)

[Arithela]

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]

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]

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]

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]

thanks all!

 

[Arithela]

what is the range of 1 -3cos2x?

do we have to change signs because its negative?

 

[lsam]

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]

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]

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.)