trig equation questions (1 Viewer)

[jane1820]

guys does anyone know a textbook that offers trig equation questions but the one where you need to change the domian
like the ones that are 'sin(2x)=1/2 in [0, 180], find x' and then ull have to change the domain (lowkey idk what im on abt)

my teacher couldnt find questions like that (we only did one in class) and told me to find them myself but i dont wanna do exam questions yet

love jane

 

[Study to success]

guys does anyone know a textbook that offers trig equation questions but the one where you need to change the domian
like the ones that are 'sin(2x)=1/2 in [0, 180], find x' and then ull have to change the domain (lowkey idk what im on abt)

my teacher couldnt find questions like that (we only did one in class) and told me to find them myself but i dont wanna do exam questions yet

love jane

I think the maths in focus one might have some idk. But I remember my teacher went through some of these

 

[C2H6O]

hopefully this is what you were after:
also i never learned the domain change method, what i would recommend is use the general solutions theyre much easier and not that hard to memorise. but ofc if this method works for you already dont waste time learning a new method.



Yes this is out of syllabus and you don't have to memorise it but my teacher taught it anyway and I find it really helpful. I hope I'm not confusing you here, but essentially you can apply these solutions to any trig problem and it can find all solutions when you plug in integers of n, kind of like guessing roots of a polynomial, until you have exhausted all possible solutions in the original domain of x.

 

[jane1820]

hopefully this is what you were after:
also i never learned the domain change method, what i would recommend is use the general solutions theyre much easier and not that hard to memorise. but ofc if this method works for you already dont waste time learning a new method.



Yes this is out of syllabus and you don't have to memorise it but my teacher taught it anyway and I find it really helpful. I hope I'm not confusing you here, but essentially you can apply these solutions to any trig problem and it can find all solutions when you plug in integers of n, kind of like guessing roots of a polynomial, until you have exhausted all possible solutions in the original domain of x.

for the domain change i just know that if its sin2x in [0,360] you would do the domain*2
so it becomes [0,720]
same with any value you just multiply the domain by the coefficient of the x

also i dont seem to understand ur method lmao
thx for the questions tho!

 

[C2H6O]

wait a sec i just realised those worksheets i gave are year 12, are you able to do them or do you need the year 11 versions (i lowkey have no idea what the maths syllabus looks like)

 

[coolcat6778]

guys does anyone know a textbook that offers trig equation questions but the one where you need to change the domian
like the ones that are 'sin(2x)=1/2 in [0, 180], find x' and then ull have to change the domain (lowkey idk what im on abt)

my teacher couldnt find questions like that (we only did one in class) and told me to find them myself but i dont wanna do exam questions yet

love jane

Maths in focus lol. Fuck the cambridge textbook.

I purely learnt about those equations from math in focus

So here's how to do it:

sin(2x)=1/2 in [0, 180]

since its 2x it means twice so [0, 360]

then you solve for 2x, which you get 30 degrees and 150 degrees by using ASTC diagram using the new domain

solve for x you get 15 degrees and 75 degrees

convert that to radians by dividing 15 by 180 and 75 by 180 and add a pi sign on top

1pi/12 and 5pi/12

This is how I always do it.




The cambridge textbook is absolutely awful for math advanced. I'm actually surprised it doesn't have those equations given how much people glaze it

 

[coolcat6778]

An equation like this is not in any textbook at all

 

[coolcat6778]

guys does anyone know a textbook that offers trig equation questions but the one where you need to change the domian
like the ones that are 'sin(2x)=1/2 in [0, 180], find x' and then ull have to change the domain (lowkey idk what im on abt)

my teacher couldnt find questions like that (we only did one in class) and told me to find them myself but i dont wanna do exam questions yet

love jane

page 105 of the year 12 math in focus advanced textbook

 

[coolcat6778]

hopefully this is what you were after:
also i never learned the domain change method, what i would recommend is use the general solutions theyre much easier and not that hard to memorise. but ofc if this method works for you already dont waste time learning a new method.



Yes this is out of syllabus and you don't have to memorise it but my teacher taught it anyway and I find it really helpful. I hope I'm not confusing you here, but essentially you can apply these solutions to any trig problem and it can find all solutions when you plug in integers of n, kind of like guessing roots of a polynomial, until you have exhausted all possible solutions in the original domain of x.

I'm sorry @C2H6O this method is genuinely awful. You're better off learning the simple extension 1 "auxilary angle" method made for these specific questions even if u only do advanced, which will be allowed in advanced exams anyway

Also I doubt this question can even appear in a HSC Advanced paper because this definitely provides a large disadvantage to Advanced only students since Extension 1 were explicitly taught how to solve these very equations using the auxilary angle method

 

[C2H6O]

View attachment 48622
I'm sorry @C2H6O this method is genuinely awful. You're better off learning the simple extension 1 "auxilary angle" method made for these specific questions even if u only do advanced, which will be allowed in advanced exams anyway

Also I doubt this question can even appear in a HSC Advanced paper because this definitely provides disadvantage to Advanced students since Extension 1 were explicitly taught how to solve these very equations using the auxilary angle method

yes i always use the auxillary angle method but my teacher put the long way for adv kids
unless you're referring to the use of the general solutions in which case we'd have to agree to disagree

 

[jane1820]

wait a sec i just realised those worksheets i gave are year 12, are you able to do them or do you need the year 11 versions (i lowkey have no idea what the maths syllabus looks like)

they're solvable dw