The Student Room Group
Uni students - Complete our survey >>
Uni students - Complete our survey >>
Uni students - Complete our survey >>

Maths C3 - Trigonometry... Help??

Scroll to see replies

Original post by RDKGames
No need, the quadratic is all in terms of a single unknown variable and that's as simple as it gets.


OMG, I actually got it :smile:

Thank you thank you thank you thank you thank you :smile:

So happy!!
Original post by Philip-flop
OMG, I actually got it :smile:

Thank you thank you thank you thank you thank you :smile:

So happy!!


No problem, well done. :smile:
How have I been stuck on Chapter 6: Trigonometry of the Edexcel C3 Modular Maths Textbook for so long? Feel's like it's taking me ages to get through the book :frown: I was hoping to have finished all of it by now!
Original post by Philip-flop
How have I been stuck on Chapter 6: Trigonometry of the Edexcel C3 Modular Maths Textbook for so long? Feel's like it's taking me ages to get through the book :frown: I was hoping to have finished all of it by now!


Anything particular that you're stuck on?
Original post by RDKGames
Anything particular that you're stuck on?

Practically everything! :P

I'm constantly asking for help and still make stupid little mistakes. Feel like I have no hope of succeeding at A2 :frown: Barely even succeeded at AS!!

Feel like I need a tutor but really can't afford it :/
(edited 7 years ago)
Original post by Philip-flop
Practically everything! :P

I'm constantly asking for help and still make stupid little mistakes. Feel like I have no hope of succeeding at A2 :frown: Barely even succeeded at AS!!


Just practice otherwise you'll carry those stupid little mistakes to the exam which is not what you want. :smile:
Original post by RDKGames
Just practice otherwise you'll carry those stupid little mistakes to the exam which is not what you want. :smile:


Yeah true. But sometimes I feel like I'm practicing loads and loads but still struggle later on :/

How do I make sure I don't lose motivation?
Original post by Philip-flop
Yeah true. But sometimes I feel like I'm practicing loads and loads but still struggle later on :/

How do I make sure I don't lose motivation?


Er, dunno. If I don't succeed in one question, I learn from it, and take on then next one because I want to get it right, I suppose. Exams are still a loooong way away so you'll get it by then.
Original post by RDKGames
Er, dunno. If I don't succeed in one question, I learn from it, and take on then next one because I want to get it right, I suppose. Exams are still a loooong way away so you'll get it by then.


Yeah, I guess I've just got to keep powering my way through and learn from my mistakes. But I seem to struggle to get the answer in the first place unless you're there prompting me like you have been :colondollar:

That's true, exams are a long way away, but in terms of the time that I have, I don't actually have a lot of study time :frown:
Ok so I'm stuck on Example 13 from chapter 6 of the Edexcel C3 Modular Maths Textbook part (a) ... For now :P ... Anyway I have a lot of questions to ask about this so if anyone could help I'd be more than thankful :smile:

C3 - Trig Identities.png

1) What gives the impression that ... cosec4θ−cot⁡4θ \mathrm{cosec}^4 \theta - \cot ^4 \theta is the difference of two squares??

2) With this situation how do you find the difference of two squares, as I only know how to when an equation is in the form Ax2−bAx^2-b

3) How/where is the identity 1+cot⁡2θ=cosec2θ1+\cot ^2 \theta = \mathrm{cosec}^2 \theta is being used??


Again, sorry for the ridiculously silly questions :/
Reply 70
Avatar for Zacken
Zacken
22
Original post by Philip-flop
Ok so I'm stuck on Example 13 from chapter 6 of the Edexcel C3 Modular Maths Textbook part (a) ... For now :P ... Anyway I have a lot of questions to ask about this so if anyone could help I'd be more than thankful :smile:


1) What gives the impression that ... cosec4θ−cot⁡4θ \mathrm{cosec}^4 \theta - \cot ^4 \theta is the difference of two squares??

2) With this situation how do you find the difference of two squares, as I only know how to when an equation is in the form Ax2−bAx^2-b

3) How/where is the identity 1+cot⁡2θ=cosec2θ1+\cot ^2 \theta = \mathrm{cosec}^2 \theta is being used??


A difference of two squares is this: a2−b2=(a−b)(a+b)a^2 - b^2 = (a-b)(a+b).

Here you have
Unparseable latex formula:

(\csc^2 \theta)^2 - (\cot^2 \theta)^2 = (\csc^2 \theta - \cot^2 \theta)(\csc^2 \thetaa + \cot^2 \theta)

.

Now the first bracket is csc⁡2θ−cot⁡2θ\csc^2 \theta - \cot^2 \theta but from your identity you know that csc⁡2θ=cot⁡2θ+1\csc^2 \theta = \cot^2 \theta + 1 so subtracting cot⁡2\cot^2 from both sides, we have csc⁡2θ−cot⁡2θ=1\csc^2 \theta - \cot^2 \theta = 1.

So your factorisation becomes (1)(csc⁡2θ+cot⁡2θ)(1)(\csc^2 \theta + \cot^2 \theta)
Original post by Philip-flop
Ok so I'm stuck on Example 13 from chapter 6 of the Edexcel C3 Modular Maths Textbook part (a) ... For now :P ... Anyway I have a lot of questions to ask about this so if anyone could help I'd be more than thankful :smile:


1) What gives the impression that ... cosec4θ−cot⁡4θ \mathrm{cosec}^4 \theta - \cot ^4 \theta is the difference of two squares??

2) With this situation how do you find the difference of two squares, as I only know how to when an equation is in the form Ax2−bAx^2-b

3) How/where is the identity 1+cot⁡2θ=cosec2θ1+\cot ^2 \theta = \mathrm{cosec}^2 \theta is being used??


Again, sorry for the ridiculously silly questions :/


1) Because both terms have the same even power and the whole expression is a difference. For any even power you can factor out a 2 which would make some arbitrary term to the power of 2, ie a square. So something like a6=(a3)2a^6=(a^3)^2 which is a square of some term to the third power.

2) cosec4θ−cot4θ=(cosec2θ)2−(cot2θ)2=...\mathrm{cosec^4 \theta} - \mathrm{cot^4 \theta} = (\mathrm{cosec^2 \theta})^2-(\mathrm{cot^2 \theta})^2=...

Also Ax2−bAx^2-b is not a form for a difference of two squares.. Difference of two squares is a2−b2=(a+b)(a−b)a^2-b^2=(a+b)(a-b). So something like A2x2−b2A^2x^2-b^2 would indeed be a difference of two squares because A2x2=(Ax)2A^2x^2=(Ax)^2

3) Second line. Second bracket equals 1.
(edited 7 years ago)
Reply 72
Avatar for Zacken
Zacken
22
Original post by RDKGames
3) Second line. Second bracket equals 0.


..
Original post by Zacken
..


lol...
Original post by RDKGames
1) Because both terms have the same even power and the whole expression is a difference. For any even power you can factor out a 2 which would make some arbitrary term to the power of 2, ie a square. So something like a6=(a3)2a^6=(a^3)^2 which is a square of some term to the third power.

2) cosec4θ−cot4θ=(cosec2θ)2−(cot2θ)2=...\mathrm{cosec^4 \theta} - \mathrm{cot^4 \theta} = (\mathrm{cosec^2 \theta})^2-(\mathrm{cot^2 \theta})^2=... try this.

Also Ax−bAx-b is not a form for a difference of two squares.. Difference of two squares is a2−b2=(a+b)(a−b)a^2-b^2=(a+b)(a-b)

3) Second line. Second bracket equals 1.


Oh yeah. The difference of two squares never really made perfect sense to me until now. Thank you! I only knew how to solve the difference of two squares if it was written for example as... x2−4=(x+2)(x−2)x^2-4 = (x+2)(x-2) but that's as basic as I could work out :frown:

Original post by Zacken
A difference of two squares is this: a2−b2=(a−b)(a+b)a^2 - b^2 = (a-b)(a+b).

Here you have
Unparseable latex formula:

(\csc^2 \theta)^2 - (\cot^2 \theta)^2 = (\csc^2 \theta - \cot^2 \theta)(\csc^2 \thetaa + \cot^2 \theta)

.

Now the first bracket is csc⁡2θ−cot⁡2θ\csc^2 \theta - \cot^2 \theta but from your identity you know that csc⁡2θ=cot⁡2θ+1\csc^2 \theta = \cot^2 \theta + 1 so subtracting cot⁡2\cot^2 from both sides, we have csc⁡2θ−cot⁡2θ=1\csc^2 \theta - \cot^2 \theta = 1.

So your factorisation becomes (1)(csc⁡2θ+cot⁡2θ)(1)(\csc^2 \theta + \cot^2 \theta)

Thank you!!! That step by step process has really helped me!! These new Trig Identities that are introduced in C3 are really intimidating but I'm glad you're there to help :smile: I just need to keep familiarising myself. Hopefully it won't be too much of a struggle :doh:
Trying to understand how for part (b) that...
sin2θ+tan2θsin^2 \theta +tan^2 \theta <<<goes from...
...to this... (1−cos2θ)+(sec⁡2θ−1)(1-cos^2 \theta)+(\sec ^2 \theta -1)
:frown:

Edit: False alarm, I was being stupid. I realised that I just had to re-arrange using Trig Identities :colondollar:
Edit: False alarm, I was being stupid. I realised that I just had to re-arrange using Trig Identities :colondollar:

C3 - Trig Identities.png

Edit: False alarm, I was being stupid. I realised that I just had to re-arrange using Trig Identities :colondollar:
(edited 7 years ago)
Original post by Philip-flop
Trying to understand how for part (b) that...
sin2θ+tan2θsin^2 \theta +tan^2 \theta <<<goes from...
...to this... (1−cos2θ)+(sec⁡2θ−1)(1-cos^2 \theta)+(\sec ^2 \theta -1)
:frown:


Because
cos⁡2θ+sin⁡2θ≡1\cos^2 \theta + \sin^2 \theta \equiv 1

and (from dividing both sides by cos squared)

1+tan⁡2θ≡sec⁡2θ1+\tan^2 \theta \equiv \sec^2 \theta

Rearrange for sine squared, and tan squared, then sub them in.
(edited 7 years ago)
Original post by RDKGames
Because
cos⁡2θ+sin⁡2θ≡1\cos^2 \theta + \sin^2 \theta \equiv 1

and (from dividing both sides by cos squared)

1+tan⁡2θ≡sec⁡2θ1+\tan^2 \theta \equiv \sec^2 \theta

Rearrange for cos squared, and tan squared, then sub it in.

Thank you. I think all these Trig Identities are making me lose my mind which is why I've been making silly mistakes like that! :colondollar:
Original post by Philip-flop
Thank you. I think all these Trig Identities are making me lose my mind which is why I've been making silly mistakes like that! :colondollar:


As long as you remember sin⁡2θ+cos⁡2θ≡1\sin^2 \theta + \cos^2 \theta \equiv 1 you can pretty much derive the rest from it so you don't necessarily have to remember all of them.
(edited 7 years ago)
Original post by RDKGames
As long as you remember sin⁡2θ+cos⁡2θ≡1\sin^2 \theta + \cos^2 \theta \equiv 1 you can pretty much derive the rest from it so you don't necessarily have to remember all of them.

Oh really? Can you explain. I'm not sure I see how the other identities are derived from that. I see them all as separate identities which is why I find it difficult to remember them :frown:

Quick Reply

Related discussions

Latest

Trending

Trending

Articles for you