Hey there! Sign in to join this conversationNew here? Join for free
    • Thread Starter
    Offline

    9
    ReputationRep:
    Find all values of θ in the range 0° ≤ θ ≤ 360° satisfying
    7/cosθ - 10/sinθ = 0

    I recognise that you use the identity tanθ = sinθ/cosθ
    but how is it tanθ= 10/7???

    7/cosθ=10/sinθ then what do you do? I need the steps please! It's just that I am revising Core 2 stuff for my resit exam and I've completely forgotten what to do!
    Please help. Thanks.
    Offline

    1
    ReputationRep:
    Start by cross multipling your 7/cosθ=10/sinθ (Multiply both sides by cosθsinθ) and simplify this.

    Now, try looking at your identity of tanθ = sinθ/cosθ.

    Can you rearrange this to get it in terms of sinθ = ?

    Then, try replacing what you get for sinθ into your cross multiplied equation and rearrange it so you get tanθ = 10/7.

    Do you wanna try this for me and see if you can get it?
    • Thread Starter
    Offline

    9
    ReputationRep:
    (Original post by backtraced)
    Start by cross multipling your 7/cosθ=10/sinθ (Multiply both sides by cosθsinθ) and simplify this.

    Now, try looking at your identity of tanθ = sinθ/cosθ.

    Can you rearrange this to get it in terms of sinθ = ?

    Then, try replacing what you get for sinθ into your cross multiplied equation and rearrange it so you get tanθ = 10/7.

    Do you wanna try this for me and see if you can get it?
    7sinθ=10cosθ
    sinθ=10cosθ/7

    tanθ=10cosθ/7/cosθ

    I'm sorry, I just can't figure this out for some reason.
    • Thread Starter
    Offline

    9
    ReputationRep:
    tanθ= 10cosθ/7 * 1/cosθ and then the cosθ's get cancelled out?? 10cosθ/7cosθ 10/7
    Offline

    3
    ReputationRep:
    (Original post by BubbleLover98)
    tanθ= 10cosθ/7 * 1/cosθ and then the cosθ's get cancelled out?? 10cosθ/7cosθ 10/7
    easy multiply everything by cosθ and sinθ
    move cosθ onto the other side
    divide both sides by 7 and cosθ at the same time
    you have  \tan \theta = \dfrac {10}{7}
    Offline

    1
    ReputationRep:
    (Original post by BubbleLover98)
    tanθ= 10cosθ/7 * 1/cosθ and then the cosθ's get cancelled out?? 10cosθ/7cosθ 10/7
    Yeah, that's it!

    A bit of an easier way to do it (or the longer way that I did it) was like this:
    7sinθ=10cosθ

    tanθ = sinθ/cosθ
    So, sinθ = tanθ*cosθ


    Plug this in to 7sinθ=10cosθ
    7tanθ*cosθ=10cosθ

    Divide both sides by cosθ
    7tanθ=10

    Divide through by 7
    tanθ=10/7

    I find it a bit easier to go through step by step, hopefully that helps a little!
    Offline

    3
    ReputationRep:
    (Original post by BubbleLover98)
    tanθ= 10cosθ/7 * 1/cosθ and then the cosθ's get cancelled out?? 10cosθ/7cosθ 10/7
    (Original post by backtraced)
    Yeah, that's it!

    A bit of an easier way to do it (or the longer way that I did it) was like this:
    7sinθ=10cosθ

    tanθ = sinθ/cosθ
    So, sinθ = tanθ*cosθ


    Plug this in to 7sinθ=10cosθ
    7tanθ*cosθ=10cosθ

    Divide both sides by cosθ
    7tanθ=10

    Divide through by 7
    tanθ=10/7

    I find it a bit easier to go through step by step, hopefully that helps a little!
    imma latex this, and get some practise..

    \dfrac {7}{\cos \theta} - \dfrac {10}{\sin \theta} = 0

     7\sin \theta - 10\cos \theta = 0

    7\sin \theta = 10 \cos \theta

     \dfrac {\sin \theta}{\cos \theta} = \dfrac {10}{7}

    done
    Offline

    2
    ReputationRep:
    Let's tackle it in another way.
    Let's use a property of proportions which goes like this:
    \frac{a}{b}=\frac{c}{d} \leftrightarrow \frac{a}{c}=\frac{b}{d}
    Offline

    1
    ReputationRep:
    Looking at it, my way was much more complicated than it needed to be - i'm sorry!

    Try looking at thefatone and depymak's work for an easier way to do it. Sorry again for being longwinded!
    Offline

    3
    ReputationRep:
    (Original post by depymak)
    Let's tackle it in another way.
    Let's use a property of proportions which goes like this:
    \dfrac{a}{b}=\dfrac{c}{d} \leftrightarrow \dfrac{a}{c}=\dfrac{b}{d}
    put a d in front of your \frac it makes them bigger like so ^^
    Offline

    2
    ReputationRep:
    or
    \frac{a}{b}=\frac{c}{d} \leftrightarrow \frac{d}{b}=\frac{c}{a}
    (Original post by depymak)
    Let's tackle it in another way.
    Let's use a property of proportions which goes like this:
    \frac{a}{b}=\frac{c}{d} \leftrightarrow \frac{a}{c}=\frac{b}{d}
    Offline

    22
    ReputationRep:
    (Original post by depymak)
    Let's tackle it in another way.
    Let's use a property of proportions which goes like this:
    \frac{a}{b}=\frac{c}{d} \leftrightarrow \frac{a}{c}=\frac{b}{d}
    The arrow you're using isn't the one you want to be, that's just incorrect notation. Logical connectives are notated as double-barred arrows, so \implies (or \Rightarrow) or \iff.
    Offline

    2
    ReputationRep:
    You are right. I tried \Leftrightarrow but something didn't go well. But after your answer, I have just found out why. Thank you.
    (Original post by Zacken)
    The arrow you're using isn't the one you want to be, that's just incorrect notation. Logical connectives are notated as double-barred arrows, so \implies (or \Rightarrow) or \iff.
    Offline

    22
    ReputationRep:
    (Original post by thefatone)
    put a d in front of your \frac it makes them bigger like so ^^
    Or just use \displaystyle...
    Offline

    3
    ReputationRep:
    (Original post by Zacken)
    Or just use \displaystyle...
    that's the one
    Offline

    22
    ReputationRep:
    (Original post by thefatone)
    that's the one
    :yep:
 
 
 
  • See more of what you like on The Student Room

    You can personalise what you see on TSR. Tell us a little about yourself to get started.

  • What newspaper do you read/prefer?
    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
  • See more of what you like on The Student Room

    You can personalise what you see on TSR. Tell us a little about yourself to get started.

  • 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.