Join TSR now and get all your revision questions answeredSign up now

Maths C3 - Trigonometry... Help??

    • Thread Starter
    Offline

    3
    ReputationRep:
    So I've decided to make a thread for when I'm working through Chapter 6: Trigonometry of the Edexcel C3 Modular Maths Textbook so I can keep posting questions I need help on here instead of posting a new thread every time. I'm self-taught Maths so you will need to be patient!

    My first problem I have encountered whilst eating lunch is this...


    Q) Work out the exact values (in surd form) of sec(210)

    The textbook shows in the example that a Quadrant/Cast Diagram has been used, but is different to the way I've learnt/used it for C2. I thought... \sec \theta = \frac{1}{\cos \theta} which means since cos is used it should appear in the 4th quadrant of the diagram? I'm so confused as to why it's been used this way

    Name:  C3 Chapt.6 EXA2 Q(a).png
Views: 324
Size:  10.8 KB
    Offline

    2
    ReputationRep:
    (Original post by Philip-flop)
    So I've decided to make a thread for when I'm working through Chapter 6: Trigonometry of the Edexcel C3 Modular Maths Textbook so I can keep posting questions I need help on here instead of posting a new thread every time. I'm self-taught Maths so you will need to be patient!

    My first problem I have encountered whilst eating lunch is this...


    Q) Work out the exact values (in surd form) of sec(210)

    The textbook shows in the example that a Quadrant/Cast Diagram has been used, but is different to the way I've learnt/used it for C2. I thought... \sec \theta = \frac{1}{\cos \theta} which means since cos is used it should appear in the 4th quadrant of the diagram? I'm so confused as to why it's been used this way

    Name:  C3 Chapt.6 EXA2 Q(a).png
Views: 324
Size:  10.8 KB
    I've never really bothered to learn the quadrant diagram - you can solve all the problems without it
    remember sec(x) = 1/cos(x)
    that cos(x)=-cos(180+x) (easily derived from cos graph)
    and that cos(30)=root(3)/2
    and you should be able to solve it
    Offline

    3
    ReputationRep:
    writing C in the 4th quadrant just means that Cos is positive in the 4th quadrant. Angles in all the quadrants have Cosines.

    cos 210° will be negative cos ( :teehee: ) 210° is in the 3rd quadrant.*
    Offline

    3
    ReputationRep:
    Eating lunch while doing maths has been scientifically been proven to lead to confusion. Don't do it.
    Offline

    3
    ReputationRep:
    (Original post by Philip-flop)
    So I've decided to make a thread for when I'm working through Chapter 6: Trigonometry of the Edexcel C3 Modular Maths Textbook so I can keep posting questions I need help on here instead of posting a new thread every time. I'm self-taught Maths so you will need to be patient!

    My first problem I have encountered whilst eating lunch is this...


    Q) Work out the exact values (in surd form) of sec(210)

    The textbook shows in the example that a Quadrant/Cast Diagram has been used, but is different to the way I've learnt/used it for C2. I thought... \sec \theta = \frac{1}{\cos \theta} which means since cos is used it should appear in the 4th quadrant of the diagram? I'm so confused as to why it's been used this way
    Ignoring signs (plus or minus), sin/cos/tan are equal in each of the four quadrants. This is shown below if you draw an X in the CAST diagram:



    E.g. let's say the acute angle is 30. This means that ignoring signs:

    \displaystyle \sin(30) = \sin(180-30) = \sin(180 + 30) = \sin(360-30).

    These are the four angles represented in the X of the cast diagram above if you travel anti-clockwise.


    And since \sin(30) = \frac{1}{2}, ignoring signs \sin(30) = \sin(150) = \sin(210) = \sin(330)  = \frac{1}{2}.

    The letters A, C, T, S tell you whether it will be \frac{1}{2} or -\frac{1}{2}

    E.g. 210 is an angle in the 'T' quadrant which means that only tan is positive so sin must be negative. So \displaystyle \sin(210) = -\frac{1}{2}.


    The example you posted has done a similar thing to find \cos(210).

    For people who struggle with the CAST diagram, I recommend drawing the X and thinking about the four angles.
    • Thread Starter
    Offline

    3
    ReputationRep:
    (Original post by notnek)
    Ignoring signs (plus or minus), sin/cos/tan are equal in each of the four quadrants. This is shown below if you draw an X in the CAST diagram:



    E.g. let's say the acute angle is 30. This means that ignoring signs:

    \displaystyle \sin(30) = \sin(180-30) = \sin(180 + 30) = \sin(360-30).

    These are the four angles represented in the X of the cast diagram above if you travel anti-clockwise.


    And since \sin(30) = \frac{1}{2}, ignoring signs \sin(30) = \sin(150) = \sin(210) = \sin(330)  = \frac{1}{2}.

    The letters A, C, T, S tell you whether it will be \frac{1}{2} or -\frac{1}{2}

    E.g. 210 is an angle in the 'T' quadrant which means that only tan is positive so sin must be negative. So \displaystyle \sin(210) = -\frac{1}{2}.


    The example you posted has done a similar thing to find \cos(210).

    For people who struggle with the CAST diagram, I recommend drawing the X and thinking about the four angles.
    Wow, that was a brilliant explanation!! You really cleared that up for me

    So for example... cosine would be positive in the c quadrant but negative in a,s, and t?
    • Thread Starter
    Offline

    3
    ReputationRep:
    (Original post by RDKGames)
    Eating lunch while doing maths has been scientifically been proven to lead to confusion. Don't do it.
    But I have to study every chance I get
    Offline

    3
    ReputationRep:
    (Original post by Philip-flop)
    So for example... cosine would be positive in the c quadrant but negative in a,s, and t?
    Not quite!

    Cosine is positive in C and A(ll).

    So basically the reason why the quadrants are named CAST is for cosine, all, sine, tangent.

    Everything is positive in the "all" or "A" quadrant.

    Sine is positive in the "sine" or "S" and "all" or "A" quadrants.

    Cosine is positive in the "cosine" or "C" and "all" or "A" quadrants.

    Tangent is positive in the "tangent" or "R" and "all" or "A" quadrants.

    This is just a helpful way to remember what's what, but I do suggest re-reading Notneks post and making sure you understand everything instead of relying on memorisation techniques as above.
    • Thread Starter
    Offline

    3
    ReputationRep:
    (Original post by Zacken)
    Not quite!

    Cosine is positive in C and A(ll).

    So basically the reason why the quadrants are named CAST is for cosine, all, sine, tangent.

    Everything is positive in the "all" or "A" quadrant.

    Sine is positive in the "sine" or "S" and "all" or "A" quadrants.

    Cosine is positive in the "cosine" or "C" and "all" or "A" quadrants.

    Tangent is positive in the "tangent" or "R" and "all" or "A" quadrants.

    This is just a helpful way to remember what's what, but I do suggest re-reading Notneks post and making sure you understand everything instead of relying on memorisation techniques as above.
    Oh yeah of course!! I am definitely a bit rusty when in comes to CAST diagrams! I'm still trying to understand why things are the way they are instead of just remembering. But as you can see I'm struggling

    I can follow what notnek is saying but I can't completely understand why things are. Like, putting quadrant diagrams aside, I struggle to understand what sin, cos, and tan really is. I know their layout on a stereotypical graph between -360<x<360 but other than typing them into a calculator I'm not sure what their purpose is. cos and sin just look like sound waves to me.
    • Thread Starter
    Offline

    3
    ReputationRep:
    Silly question but is...

    A the 1st quadrant
    S the 2nd quadrant
    T the 3rd quadrant
    C the 4th quadrant

    on a cast diagram?
    Offline

    3
    ReputationRep:
    (Original post by Philip-flop)
    Silly question but is...

    A the 1st quadrant
    S the 2nd quadrant
    T the 3rd quadrant
    C the 4th quadrant

    on a cast diagram?
    Yep.
    • Thread Starter
    Offline

    3
    ReputationRep:
    Can someone please tell me what this means?...

    n\in \mathbb{Z}

    I know that x\in\mathbb{R} << means that x is any real number. But I don't know what the bit above means
    Offline

    2
    ReputationRep:
    (Original post by Philip-flop)
    Can someone please tell me what this means?...

    n\in \mathbb{Z}

    I know that x\in\mathbb{Z} << means that x is any real number. But I don't know what the bit above means
    it means n is an integer (n is an element of z (the integer set))
    and the second one means that x is an integer, not any real number
    Offline

    3
    ReputationRep:
    (Original post by Philip-flop)
    Can someone please tell me what this means?...

    n\in \mathbb{Z}

    I know that x\in\mathbb{Z} << means that x is any real number. But I don't know what the bit above means
    Don't get confused.

    http://www.math.ku.edu/~porter/Math_symbols%20.pdf
    • Thread Starter
    Offline

    3
    ReputationRep:
    Sorry guys I made a typo.. I meant

    What does this mean?...
    n\in\mathbb{Z}

    I know that x\in\mathbb{R} << means that x is any real number
    • Thread Starter
    Offline

    3
    ReputationRep:
    Wow thanks for that link! Super useful!!
    Offline

    2
    ReputationRep:
    Hey, in your C3 book, there's a small section called "Lists of symbols and notation". This section is just before the Answers so I'd advise you to use it if you ever need it!
    • Thread Starter
    Offline

    3
    ReputationRep:
    (Original post by ManLike007)
    Hey, in your C3 book, there's a small section called "Lists of symbols and notation". This section is just before the Answers so I'd advise you to use it if you ever need it!
    Thank you, I never realised that section in the book before!!
    • Thread Starter
    Offline

    3
    ReputationRep:
    Can someone please explain to me using Trig identities how this...
    \sec \theta = -2.5

    becomes...

    \cos \theta =-0.4

    I'm so confused. I know that \sec \theta = \frac{1}{\cos \theta}
    which can be rearranged to make \cos \theta = \frac{1}{\sec \theta}
    Offline

    2
    ReputationRep:
    (Original post by Philip-flop)
    Can someone please explain to me using Trig identities how this...
    \sec \theta = -2.5

    becomes...

    \cos \theta =-0.4

    I'm so confused. I know that \sec \theta = \frac{1}{\cos \theta}
    which can be rearranged to make \cos \theta = \frac{1}{\sec \theta}
    sec(theta)=-2.5
    cos(theta)=1/sec(theta)=1/(-2.5)=-0.4
 
 
 
Poll
Which party will you be voting for in the General Election 2017?
Useful resources

Make your revision easier

Maths

Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here

Equations

How to use LaTex

Writing equations the easy way

Student revising

Study habits of A* students

Top tips from students who have already aced their exams

Study Planner

Create your own Study Planner

Never miss a deadline again

Polling station sign

Thinking about a maths degree?

Chat with other maths applicants

Can you help? Study help unanswered threads

Groups associated with this forum:

View associated groups

The Student Room, Get Revising and Marked by Teachers are trading names of The Student Room Group Ltd.

Register Number: 04666380 (England and Wales), VAT No. 806 8067 22 Registered Office: International House, Queens Road, Brighton, BN1 3XE

Quick reply
Reputation gems: You get these gems as you gain rep from other members for making good contributions and giving helpful advice.