Turn on thread page Beta
    • Thread Starter
    Offline

    0
    ReputationRep:
    if cosX = -8/17 and X is obtuse, find the values of
    a) cotX b)cosecX


    and


    Solve for -180<X<180

    secX = 2cosX

    :confused:
    Offline

    8
    ReputationRep:
    Setp 1 - find x from

     x = arccos(\frac{-8}{17}) = 118 degrees

    Now put this value of x into parts a) and b) to get answer.

    for second part

     sec x = \frac{1}{cosx} so multiply through equation by cos x

     1 = 2 cos^2x

    then solve this!
    • Thread Starter
    Offline

    0
    ReputationRep:
    (Original post by spread_logic_not_hate)
    Setp 1 - find x from

     x = arccos(\frac{-8}{17}) = 118 degrees

    Now put this value of x into parts a) and b) to get answer.

    for second part

     sec x = \frac{1}{cosx} so multiply through equation by cos x

     1 = 2 cos^2x

    then solve this!
    amazing.
    how do i solve the second part though

    i cant believe i missed out on trig!
    Offline

    8
    ReputationRep:
     cos^2x = \frac{1}{2}

    so

     cosx = \frac{1}{\sqrt 2}

    which means that

     x = arccos(\frac{1}{\sqrt 2}) = 45 degrees

    question wants all of the solutions between -180 and 180, so using that cos(x) is symmetric about the y axis (meaning  cosx = cos(-x) ) the other solution is  x = -45

 degrees.

    We need not consider any further solutions due to the restricted range of answers (-180 to 180) as cos(x) repeats every 360 degrees, so next solution would be outside range.

    EDIT

    sorry thats rubbish - the solutions are actually

     cosx = \pm\frac{1}{\sqrt 2}

    so also consider  x = arccos(-\frac{1}{\sqrt 2})

    Sorry about that, totally forgot it was a squared term!
    Offline

    0
    ReputationRep:
    (Original post by SeekerOfKnowledge)
    if cosX = -8/17 and X is obtuse, find the values of
    a) cotX b)cosecX


    and


    Solve for -180<X<180

    secX = 2cosX

    :confused:
    do you have the answers to these questions..I'm struggling to get the answer too
    • Thread Starter
    Offline

    0
    ReputationRep:
    (Original post by spread_logic_not_hate)
     cos^2x = \frac{1}{2}

    so

     cosx = \frac{1}{\sqrt 2}

    which means that

     x = arccos(\frac{1}{\sqrt 2}) = 45 degrees

    question wants all of the solutions between -180 and 180, so using that cos(x) is symmetric about the y axis (meaning  cosx = cos(-x) ) the other solution is  x = -45

 degrees.

    We need not consider any further solutions due to the restricted range of answers (-180 to 180) as cos(x) repeats every 360 degrees, so next solution would be outside range.

    EDIT

    sorry thats rubbish - the solutions are actually

     cosx = \pm\frac{1}{\sqrt 2}

    so also consider  x = arccos(-\frac{1}{\sqrt 2})

    Sorry about that, totally forgot it was a squared term!
    Great Thanks so much!
    • Thread Starter
    Offline

    0
    ReputationRep:
    (Original post by ladythugette)
    do you have the answers to these questions..I'm struggling to get the answer too
    sure

    a) -8/15 b)17/15


    for the second part: +- 45 and +-135
    • Thread Starter
    Offline

    0
    ReputationRep:
    (Original post by SeekerOfKnowledge)
    Great Thanks so much!
    how about equations where you cannoy find the identity?

    cotX = 5 cosX
    • Thread Starter
    Offline

    0
    ReputationRep:
    (Original post by spread_logic_not_hate)
     cos^2x = \frac{1}{2}

    so

     cosx = \frac{1}{\sqrt 2}

    which means that

     x = arccos(\frac{1}{\sqrt 2}) = 45 degrees

    question wants all of the solutions between -180 and 180, so using that cos(x) is symmetric about the y axis (meaning  cosx = cos(-x) ) the other solution is  x = -45

 degrees.

    We need not consider any further solutions due to the restricted range of answers (-180 to 180) as cos(x) repeats every 360 degrees, so next solution would be outside range.

    EDIT

    sorry thats rubbish - the solutions are actually

     cosx = \pm\frac{1}{\sqrt 2}

    so also consider  x = arccos(-\frac{1}{\sqrt 2})

    Sorry about that, totally forgot it was a squared term!
    how about equations where you cannoy find the identity?

    cotX = 5 cosX
    Offline

    0
    ReputationRep:
    (Original post by SeekerOfKnowledge)
    sure

    a) -8/15 b)17/15


    for the second part: +- 45 and +-135
    thank you...I finally got the answer after 10 minutes of scribbling in my note book.I really need to do some serious C3 revision tomorrow on trig before my exam on wednesday.

    good luck btw, when ever you're taking your exam.
    Offline

    8
    ReputationRep:
    Do you mean solve cot x = 5 cos x?

    If so use that

     cot x = \frac{cos x}{sin x} so

     \frac{cos x}{sin x} = 5 cos x

    rearrange to get

     sin x = \frac{1}{5}

    and then solve!
 
 
 
Reply
Submit reply
Turn on thread page Beta
Updated: January 19, 2010

University open days

  1. University of Cambridge
    Christ's College Undergraduate
    Wed, 26 Sep '18
  2. Norwich University of the Arts
    Undergraduate Open Days Undergraduate
    Fri, 28 Sep '18
  3. Edge Hill University
    Faculty of Health and Social Care Undergraduate
    Sat, 29 Sep '18
Poll
Which accompaniment is best?
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

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.