Turn on thread page Beta
    • Thread Starter
    Offline

    3
    ReputationRep:
    Express f(θ) = 5 cos θ + 12 sin θ in the form RCos (θ-α)
    I got: 13 cos (θ - 1.176)

    part b) Find the smallest possible value of  \frac{30}{ f(\theta) + 2}

    I'm completely stuck on how to do the second part, for the smallest value it would be -1 not sure how this would help me get the answer, thanks for all the help!
    Offline

    16
    ReputationRep:
    (Original post by IgorYakov)
    Express f(θ) = 5 cos θ + 12 sin θ in the form RCos (θ-α)
    I got: 13 cos (θ - 1.176)

    part b) Find the smallest possible value of  \frac{30}{ f(\theta) + 2}

    I'm completely stuck on how to do the second part, for the smallest value it would be -1 not sure how this would help me get the answer, thanks for all the help!
    What does this mean
    • Thread Starter
    Offline

    3
    ReputationRep:
    (Original post by TenOfThem)
    What does this mean

    Sorry I didn't word that properly, for the smallest value for Cos it would be -1 right? So in the case of the 13 cos (θ - 1.176) it would be -13?


    Or is this completely different to maximum and minimum values?
    Offline

    13
    ReputationRep:
    (Original post by IgorYakov)
    Express f(θ) = 5 cos θ + 12 sin θ in the form RCos (θ-α)
    I got: 13 cos (θ - 1.176)

    part b) Find the smallest possible value of  \frac{30}{ f(\theta) + 2}

    I'm completely stuck on how to do the second part, for the smallest value it would be -1 not sure how this would help me get the answer, thanks for all the help!
    f(\theta) = R\cos \left( \theta - \alpha \right), \ \text{where} \ \alpha = \text{arctan} \left( \frac{12}{5} \right) \ \text{and} \ R=13

    Which value of f(\theta) would force \frac{30}{ f(\theta) + 2} to take on it's smallest value?

    Hint
    The denominator must be forced to it's maximum, to ensure the fraction given is at it's smallest value.

    Further Hint
    -1 \leq \cos \left( \theta - \alpha \right) \leq 1 \implies -R \leq R\cos \left( \theta - \alpha \right) \leq R
    Offline

    16
    ReputationRep:
    (Original post by IgorYakov)
    Sorry I didn't word that properly, for the smallest value for Cos it would be -1 right? So in the case of the 13 cos (θ - 1.176) it would be -13?
    Your smallest value of f(theta) = -13

    So what are the smallest and largest values of f(theta) + 2
    • Thread Starter
    Offline

    3
    ReputationRep:
    (Original post by Khallil)
    f(\theta) = R\cos \left( \theta - \alpha \right), \ \text{where} \ \alpha = \text{arctan} \left( \frac{12}{5} \right) \ \text{and} \ R=13

    Which value of f(\theta) would force \frac{30}{ f(\theta) + 2} to take on it's smallest value?

    Hint
    The denominator must be forced to it's maximum, to ensure the fraction given is at it's smallest value.

    Further Hint
    -1 \leq \cos \left( \theta - \alpha \right) \leq 1 \implies -R \leq R\cos \left( \theta - \alpha \right) \leq R


    Ohh okay so for the maximum of 13 cos (θ - 1.176) it is 13 as the maximum for a cos graph is 1 ?
    • Thread Starter
    Offline

    3
    ReputationRep:
    (Original post by TenOfThem)
    Your smallest value of f(theta) = -13

    So what are the smallest and largest values of f(theta) + 2

    Wouldn't you just have one value of -13+2 for the minimum of -13?
    Offline

    16
    ReputationRep:
    (Original post by IgorYakov)
    Wouldn't you just have one value of -13+2 for the minimum of -13?
    -11 is indeed the minimum

    what is the maximum
    Offline

    13
    ReputationRep:
    (Original post by IgorYakov)
    Ohh okay so for the maximum of 13 cos (θ - 1.176) it is 13 as the maximum for a cos graph is 1 ?
    :yep:

    Now what does the fact that the maximum value of f(\theta) being 13 tell you about \frac{30}{ f(\theta) + 2} \ ?
    • Thread Starter
    Offline

    3
    ReputationRep:
    (Original post by Khallil)
    :yep:

    Now what does the fact that the maximum value of f(\theta) being 13 tell you about \frac{30}{ f(\theta) + 2} \ ?

    (Original post by TenOfThem)
    -11 is indeed the minimum

    what is the maximum


    That it's 2

    Thanks! I was trying to find the minimum and not the maximum, I didn't realise that because it's on the denominator I needed the maximum for the whole number to be it's smallest



    Khallil PRSOM
    Offline

    16
    ReputationRep:
    (Original post by Khallil)
    f(\theta) = R\cos \left( \theta - \alpha \right), \ \text{where} \ \alpha = \text{arctan} \left( \frac{12}{5} \right) \ \text{and} \ R=13

    Which value of f(\theta) would force \frac{30}{ f(\theta) + 2} to take on it's smallest value?

    Hint
    The denominator must be forced to it's maximum, to ensure the fraction given is at it's smallest value.

    Further Hint
    -1 \leq \cos \left( \theta - \alpha \right) \leq 1 \implies -R \leq R\cos \left( \theta - \alpha \right) \leq R
    You need to look at the specific question as your hint is not correct in this case
    Offline

    16
    ReputationRep:
    (Original post by IgorYakov)
    That it's 2

    Thanks! I was trying to find the minimum and not the maximum, I didn't realise that because it's on the denominator I needed the maximum for the whole number to be it's smallest
    Sorry - where have you got 2 from

    That is not the maximum for the denominator nor the answer to the question
    • Thread Starter
    Offline

    3
    ReputationRep:
    (Original post by TenOfThem)
    Sorry - where have you got 2 from

    That is not the maximum for the denominator nor the answer to the question


    As it's 13 isn't it just 30/13+2?
    Offline

    16
    ReputationRep:
    (Original post by IgorYakov)
    As it's 13 isn't it just 30/13+2?
    no
    • Thread Starter
    Offline

    3
    ReputationRep:
    (Original post by TenOfThem)
    no

    Ohh ok so what would I do after getting the maximum of 13?
    Offline

    16
    ReputationRep:
    (Original post by IgorYakov)
    Ohh ok so how what would I do after getting the maximum of 13?
    Okay

    Look at what I asked you

    What are the minimum and maximum values of f(theta) + 2
    • Thread Starter
    Offline

    3
    ReputationRep:
    (Original post by TenOfThem)
    Okay

    Look at what I asked you

    What are the minimum and maximum values of f(theta) + 2
    minimum -11, maximum 15?
    Offline

    16
    ReputationRep:
    (Original post by IgorYakov)
    minimum -11, maximum 15?
    ok - I always suggest that students consider both ends of the range

    So

    Which is smaller

    30/-11 or 30/15
    Offline

    13
    ReputationRep:
    (Original post by TenOfThem)
    Sorry - where have you got 2 from

    That is not the maximum for the denominator nor the answer to the question
    Really?

    Spoiler:
    Show
    (b) \ \text{Find the smallest possible value of} \  \frac{30}{ f(\theta) + 2}

    To find the smallest value of the given fraction, maximise the value of the denominator.

    f(\theta) = 13\cos \left( \theta - \text{arctan} \left( \frac{12}{5} \right) \right)

    The maximum value of f occurs at \theta = \text{arctan} \left( \frac{12}{5} \right) + 2\pi n

    \therefore \ f\left((\text{arctan} \left( \frac{12}{5} \right) \right) = 13

    The smallest value of the given fraction is:

    \therefore \ \dfrac{30}{13 + 2} = 2
    • Thread Starter
    Offline

    3
    ReputationRep:
    (Original post by TenOfThem)
    ok - I always suggest that students consider both ends of the range

    So

    Which is smaller

    30/-11 or 30/15
    30/-11
 
 
 
Reply
Submit reply
Turn on thread page Beta
Updated: November 15, 2013

University open days

  • University of Roehampton
    All departments Undergraduate
    Sat, 17 Nov '18
  • Edge Hill University
    Faculty of Health and Social Care Undergraduate
    Sat, 17 Nov '18
  • Bournemouth University
    Undergraduate Open Day Undergraduate
    Sat, 17 Nov '18
Poll
Black Friday: Yay or Nay?
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

Equations

Best calculators for A level Maths

Tips on which model to get

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

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