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Graph translation trig functions

It is C2 AQA. Can you help me how to sketch the graphs of:

sin(2x-180)=y

tan1/2x=y

and

1-tan1/2x=y

Please tell me how to do it :smile:
(edited 9 years ago)
Original post by CTinTin14
It is C2 AQA. Can you help me how to sketch the graphs of:

sin(2x-180)=y

tan1/2x=y

and

1-tan1/2x=y

Please tell me how to do it :smile:


Do you know how transformations of graphs for non-trig functions work? Then transforming trig is really similar, just a bit more complicated.
Reply 2
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CTinTin14
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Original post by SeanFM
Do you know how transformations of graphs for non-trig functions work? Then transforming trig is really similar, just a bit more complicated.


Yes i do know
Original post by CTinTin14
Yes i do know


Okay, so for sin(2x-180), what does the 2x do to the sin(x) graph? What happens after that's been done?

Edit: Misleading. See below.
(edited 9 years ago)
Reply 4
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CTinTin14
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Original post by SeanFM
Okay, so for sin(2x-180), what does the 2x do to the sin(x) graph? What happens after that's been done?


Stretch the graph in the X direction by 1/2
Original post by CTinTin14
Stretch the graph in the X direction by 1/2


Correct :smile: Now what does the -180 do?
Reply 6
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CTinTin14
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Original post by SeanFM
Correct :smile: Now what does the -180 do?


shifts the curve to the right, so the curve will cut at 180 :smile:
Original post by CTinTin14
shifts the curve to the right, so the curve will cut at 180 :smile:


Bingo. So can you sketch the transformation? It may help to do it in stages.
Reply 8
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CTinTin14
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Original post by SeanFM
Bingo. So can you sketch the transformation? It may help to do it in stages.


Okay. Thank you! :biggrin:

How do I do 1-tan1/2x=y
(edited 9 years ago)
Original post by SeanFM
Okay, so for sin(2x-180), what does the 2x do to the sin(x) graph? What happens after that's been done?


I'm not quite sure what you're suggesting here, but it looks to me like you are getting the order of transformation wrong. The required order is either:

x→x−180,x→2xx \rightarrow x-180, x \rightarrow 2x

or:

x→2x,x→x−90x \rightarrow 2x, x \rightarrow x-90

(since sin⁡(2x−180)=sin⁡(2(x−90))\sin(2x-180) = \sin(2(x-90)))
Original post by atsruser
I'm not quite sure what you're suggesting here, but it looks to me like you are getting the order of transformation wrong. The required order is either:

x→x−180,x→2xx \rightarrow x-180, x \rightarrow 2x

or:

x→2x,x→x−90x \rightarrow 2x, x \rightarrow x-90

(since sin⁡(2x−180)=sin⁡(2(x−90))\sin(2x-180) = \sin(2(x-90)))


I was suggesting that it was 2x first and then 180, but I must have gotten confused. Sorry.

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