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# Maths C3 - Trigonometry... Help?? Watch

1. (Original post by IrrationalRoot)
I'm assuming your 'head hurts' (lol) because you always thought had an inverse. If so, answer me this question: if , what is ? Is your answer ? Wrong, . In fact could be any even multiple of .
I thought that if then can equal either and so on. as the graph crosses the x-axis at these points when y=0

(Original post by IrrationalRoot)
Hopefully you now see why does not have an inverse. If you're given the value of , you cannot determine . is not one-to-one.
No, I know that doesn't have an exact inverse as for it to be a function it must be a one-to-one. Hence why only the domain of gets "inverted" to create the function
2. (Original post by Philip-flop)
I thought that if then can equal either and so on. as the graph crosses the x-axis at these points when y=0

No, I know that doesn't have an exact inverse as for it to be a function it must be a one-to-one. Hence why only the domain of gets "inverted" to create the function
That is all correct.
3. Are my workings right for question 5? I understand how to get the answer but wasn't too sure how to write everything down

Attachment 582432582434
Attached Images

4. (Original post by Philip-flop)
Are my workings right for question 5? I understand how to get the answer but wasn't too sure how to write everything down

Yes that is correct.

Alternatively just write:

and
5. (Original post by RDKGames)
But 0 is a multiply of so it's not wrong, it's just a principal solution, and it doesn't have to be an even multiple. It would be a mess to lead OP to general solutions of sine at this point.
Idk why I said even, sorry (but this was obviously a mistake...).
And no, what I'm saying is that I could take the number and give you the information , in which case is wrong.. This was the point.
It certainly wouldn't be 'a mess to lead OP to general solutions'. I'm not even teaching them general solutions. I was giving an example to illustrate my point, which it did.
6. (Original post by Philip-flop)
I thought that if then can equal either and so on. as the graph crosses the x-axis at these points when y=0

No, I know that doesn't have an exact inverse as for it to be a function it must be a one-to-one. Hence why only the domain of gets "inverted" to create the function
Then it doesn't make sense why you don't understand . This is a direct consequence of what you've just said.
7. (Original post by IrrationalRoot)
Idk why I said even, sorry (but this was obviously a mistake...).
And no, what I'm saying is that I could take the number and give you the information , in which case is wrong.. This was the point.
It certainly wouldn't be 'a mess to lead OP to general solutions'. I'm not even teaching them general solutions. I was giving an example to illustrate my point, which it did.
Ah okay. I do think it would be a mess based on his understanding, and decided to mention it as your point touches upon them in principle with multiples.
8. 1) (cosec2o)^2-(cot2o)^2

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9. (Original post by RDKGames)
Ah okay. I do think it would be a mess based on his understanding, and decided to mention it as your point touches upon them in principle with multiples.
I think OP can understand multiples... Anyone who has any knowledge of trig functions will understand , so this wouldn't confuse OP. It serves as a good example of the fact that is many-to-one. If I just say it's 'many-to-one' with no explanation then that would certainly be more confusing and would likely lead to 'a mess' as you put it.
10. (Original post by Philip-flop)
I thought that if then can equal either and so on. as the graph crosses the x-axis at these points when y=0

No, I know that doesn't have an exact inverse as for it to be a function it must be a one-to-one. Hence why only the domain of gets "inverted" to create the function
I must also point out that this: "for it to be a function it must be a one-to-one"
is simply wrong. There seems to still be a misunderstanding here. Unless you're talking about the inverse when you say 'it' in which case ok, but see my previous reply.
Also not sure why so much use of emboldening...
11. (Original post by Philip-flop)
Are my workings right for question 5? I understand how to get the answer but wasn't too sure how to write everything down

Attachment 582432582434
I know this is completely off topic, but I love your pi. Could you do a tutorial?
12. (Original post by IrrationalRoot)
Then it doesn't make sense why you don't understand . This is a direct consequence of what you've just said.
I'm just confused by the equation. I'm sure it's right but I can't seem to understand the layout of it. Sorry

(Original post by IrrationalRoot)
I think OP can understand multiples... Anyone who has any knowledge of trig functions will understand , so this wouldn't confuse OP. It serves as a good example of the fact that is many-to-one. If I just say it's 'many-to-one' with no explanation then that would certainly be more confusing and would likely lead to 'a mess' as you put it.
My knowledge of trig functions is, lets just say limited. I have no idea what you mean by the part where you say ... Where has that K come from??

I know that though

(Original post by IrrationalRoot)
I must also point out that this: "for it to be a function it must be a one-to-one"
is simply wrong. There seems to still be a misunderstanding here. Unless you're talking about the inverse when you say 'it' in which case ok, but see my previous reply.
Also not sure why so much use of emboldening...
How come you only quoted half of my sentence?

Let me edit a section of what I said so it is a little clearer...
sin doesn't have an exact inverse as for it (arcsin) to be a function it must be a one-to-one.
13. (Original post by asinghj)
I know this is completely off topic, but I love your pi. Could you do a tutorial?
Ah schuckkkks

Plenty more pi to go around
14. LOOL
15. just means for every even multiple of sin will equal 0

i hate latex
16. (Original post by Philip-flop)
I'm just confused by the equation. I'm sure it's right but I can't seem to understand the layout of it. Sorry

My knowledge of trig functions is, lets just say limited. I have no idea what you mean by the part where you say ... Where has that K come from??

I know that though

How come you only quoted half of my sentence?

Let me edit a section of what I said so it is a little clearer...
sin doesn't have an exact inverse as for it (arcsin) to be a function it must be a one-to-one.
just stands for any integer. So by all I'm saying is that since all these angles are full turns of a circle and will thus have the same sines.

I mentioned "Unless you're talking about the inverse when you say 'it' in which case ok." I did acknowledge what you said.
17. (Original post by IrrationalRoot)
just stands for any integer. So by all I'm saying is that since all these angles are full turns of a circle and will thus have the same sines.

I mentioned "Unless you're talking about the inverse when you say 'it' in which case ok." I did acknowledge what you said.
Oh right I see. Yeah I get you now. Learn something everyday

Thanks for being patient with me btw. I really appreciate it!!
18. (Original post by Philip-flop)
Oh right I see. Yeah I get you now. Learn something everyday

Thanks for being patient with me btw. I really appreciate it!!
Good to hear . Tbh I should be thanking you for being patient with me lol, the number of times today I've had to edit things I've said due to mistakes etc. is ridiculous...
19. (Original post by IrrationalRoot)
Good to hear . Tbh I should be thanking you for being patient with me lol, the number of times today I've had to edit things I've said due to mistakes etc. is ridiculous...
Yes it is ridiculous. Especially for someone like you, after having done so brilliantly in STEP. You should be ashamed of yourself
20. So I've just started Chapter 7 of the Edexcel C3 Modular Maths textbook and have already encountered a problem

It's about proving the 'addition formula' for cos(A-B) = cosAcosB + sinAsinB

1. Why are the coordinates of P and Q... P(cosA, sinA) and Q(cosB, sinB)?
2. Why is the radius of the circle 1?
3. Why is the angle POQ equal to (A-B)?? Surely it would be angle POQ = (B-A), is it because using the addition formulae cos(a-b) = cos(b-a)??
4. How would one know to compare the lengths of PQ^2 from the results of using the cosine rule and the distance between two coordinates for this type of question?

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