Angle reflection identities (1 Viewer)

[jinglebells1464646]

Hi everyone, So for both extension 2 and 1, which of the identities in the Reflections, shifts, and periodicity category of the wikipedia page on "List of trigonometric identities"
do I need to know? I somehow can't attach the link

 

[askit]

I wouldn't memorise any of them, if you've done transformations you understand the general way of translating and dilating a function.

 

[jinglebells1464646]

can I ask, if I got like say between 80 and 90 for the first extension 1 task, do I still have a chance to get 99+ atar?

 

[askit]

can I ask, if I got like say between 80 and 90 for the first extension 1 task, do I still have a chance to get 99+ atar?

Yeah, your first task is usually the lightest in weighting, and you still got more internals to come. The mark you get is actually irrelevant apart from the fact that it gives your ranks for school. If you ranked well in your first assessment your on track to 99. Don't sweat the actual marks cause the don't contribute to your atar. This is because multiple schools have varying difficulties and it would be unfair to just use the mark gotten by students, since teachers could write easier exams to bolster potential marks.

 

[liamkk112]

Hi everyone, So for both extension 2 and 1, which of the identities in the Reflections, shifts, and periodicity category of the wikipedia page on "List of trigonometric identities"
do I need to know? I somehow can't attach the link

you should probably know that sin and tan are odd, whereas cos is even, and that sin and cos are 2pi periodic whereas tan is pi periodic. for adding angles in the arguments like sin(x +pi/2) = cosx, just memorise the sin, cos and tan angle sum identities and then u can derive it with whichever angle.

 

[carrotsss]

can I ask, if I got like say between 80 and 90 for the first extension 1 task, do I still have a chance to get 99+ atar?

yes easily, an 80 to 90 in mx1 is actually a pretty good mark

 

[Average Boreduser]

Yeah, your first task is usually the lightest in weighting, and you still got more internals to come. The mark you get is actually irrelevant apart from the fact that it gives your ranks for school. If you ranked well in your first assessment your on track to 99. Don't sweat the actual marks cause the don't contribute to your atar. This is because multiple schools have varying difficulties and it would be unfair to just use the mark gotten by students, since teachers could write easier exams to bolster potential marks.

Is third alright for an early 100s ranked school?

 

[liamkk112]

Is third alright for an early 100s ranked school?

depends what you're aiming for but its still pretty good

 

[Average Boreduser]

depends what you're aiming for but its still pretty good

~97-98?

 

[liamkk112]

~97-98?

pretty good then, it just depends on ur cohort really, ranking isn't necessarily reflective of that. just try to internally rank as high as you can for more security

 

[jinglebells1464646]

you should probably know that sin and tan are odd, whereas cos is even, and that sin and cos are 2pi periodic whereas tan is pi periodic. for adding angles in the arguments like sin(x +pi/2) = cosx, just memorise the sin, cos and tan angle sum identities and then u can derive it with whichever angle.

could you elaborate on "angle sum identites". Did you mean compound angle formulas?

 

[Luukas.2]

could you elaborate on "angle sum identites". Did you mean compound angle formulas?

By angle sum identities, I think @liamkk112 is referring to results like:

​

All of which can be derived from the double angle formulae. For sine and cosine, this is by simple substitution:

​

However, in the case of the tangent function, it is sometimes necessary to rearrange before substitution:

​

 

[Luukas.2]

Looking at the page you mentioned, https://en.wikipedia.org/wiki/List_of_trigonometric_identities, it goes way waaaaaay beyond the formulae covered in the HSC courses (across all levels) and, as illustrated above, many of the results can be derived using other results stated.

Understanding how to derive results from known equations / identities is far more useful than memorising them, especially as the HSC exams will have a formula sheet that states all the sum and difference and double angle results. Some you will use so much that you will memorise them from sheer repetition, but they will be available to check in the HSC exams in any case. Whether your school gives you a formula sheet in every assessment is a different question, however.

 

[Luukas.2]

Or, alternatively:

​

And then, using symmetry:

​