ATAR Notes: Forum

VCE Stuff => VCE Mathematics => VCE Mathematics/Science/Technology => VCE Subjects + Help => VCE Mathematical Methods CAS => Topic started by: Andiio on February 15, 2011, 07:05:09 pm

Title: Simple trig question!
Post by: Andiio on February 15, 2011, 07:05:09 pm: When sketching circular/trigonometric functions with transformations, is it best to apply each dilation/reflection/translation etc separately? (That's what I've kinda started to do)

Also, does anyone know any 'special ways' of applying translations? (Not sure how everyone else does them.) Is it just remembering the 5 important points (period/4) and then shifting those?

Thanks!
Title: Re: Simple trig question!
Post by: luffy on February 15, 2011, 07:12:00 pm: I don't know what you mean about the transformations. How could you 'not' apply them separately?

If it helps, I always consider the dilations, then reflections and lastly translations, when writing transformations of a certain function. The order of transformations can in fact, have a large impact. So be careful.

Also, period/4?

For trigonometric functions, its best to find the amplitude and the period and work from there. Graphing trigonometric functions only gets somewhat tricky when the horizontal translation in the x-axis does not match the period.
Title: Re: Simple trig question!
Post by: luken93 on February 15, 2011, 07:21:05 pm: Yeah I usually just see if it it has any vertical translations, and if so draw an imaginary line to act like an axis
Secondly, determine the end points, x ints/y ints and if there are any vertical translations from above, work out them as well (i find it looks nicer as it is the midpoint of the trough)
Finally, just fill in the max/min gaps, and if all goes to plan, woo hoo :)
Title: Re: Simple trig question!
Post by: Andiio on February 15, 2011, 07:41:20 pm: I basically meant horizontal translations haha - I meant the separate application of transformations as drawing rough sketches of each and then continuing on. My explanation ^ was quite obscure.
Title: Re: Simple trig question!
Post by: luken93 on February 15, 2011, 07:45:39 pm: Quote from: Andiio on February 15, 2011, 07:41:20 pm
I basically meant horizontal translations haha - I meant the separate application of transformations as drawing rough sketches of each and then continuing on. My explanation ^ was quite obscure.
If you have seen DHa's method, it seems as though it is similar to yours so if you want to perfect it that is probably a good guide to learn from!
Title: Re: Simple trig question!
Post by: iNerd on February 15, 2011, 07:47:38 pm: Luken you've posted the exact same thing twice above.
Title: Re: Simple trig question!
Post by: luken93 on February 15, 2011, 07:49:19 pm: Quote from: ATAR on February 15, 2011, 07:47:38 pm
Luken you've posted the exact same thing twice above.
I'm sorry ATAR, it has now been removed.
Title: Re: Simple trig question!
Post by: iNerd on February 15, 2011, 07:49:52 pm: Quote from: luken93 on February 15, 2011, 07:49:19 pm
Quote from: ATAR on February 15, 2011, 07:47:38 pm
Luken you've posted the exact same thing twice above.
I'm sorry ATAR, it has now been removed.
No need for an apology - merely pointing it out - a thank you would have been sufficient :P
Title: Re: Simple trig question!
Post by: Romperait on February 15, 2011, 08:07:19 pm: Thank you, Atar. =)
Title: Re: Simple trig question!
Post by: luken93 on February 15, 2011, 08:38:14 pm: Quote from: Romperait on February 15, 2011, 08:07:19 pm
Thank you, Atar. =)
+1 hahaha