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

    0
    ReputationRep:
    How do you solve trigonometic equations such as secØ=3 where 0<Ø<2pi

    I know you use the trigonometric functions where you do the inverse of cos(1/3)
    But how do you find out the other value without drawing a graph?
    How do you know if you have to take it away from 2pi or just pi, or add it to pi to get the other value? :\
    • PS Helper
    Offline

    14
    Well \sec \theta = 3 if and only if \cos \theta = \dfrac{1}{3}, so the set of values of \theta in the range 0 \le \theta \le 2\pi which satisfy the equation is the same in both cases. So you don't need to worry about adding, subtracting, etc... you can just solve the cosine equation.

    For what it's worth, though, the same rules apply for sec as for cos. For example \cos (-\theta) = \cos \theta \implies \dfrac{1}{\cos (-\theta)} = \dfrac{1}{\cos \theta}, and so \sec (-\theta) = \sec \theta. Similarly, \sec (\theta + \pi) = -\sec \theta... and so on.
    Offline

    1
    ReputationRep:
    You can always sketch out a little graph in the margin or somewhere if it helps you, I do that sometimes
    • Thread Starter
    Offline

    0
    ReputationRep:
    (Original post by nuodai)
    Well \sec \theta = 3 if and only if \cos \theta = \dfrac{1}{3}, so the set of values of \theta in the range 0 \le \theta \le 2\pi which satisfy the equation is the same in both cases. So you don't need to worry about adding, subtracting, etc... you can just solve the cosine equation.

    For what it's worth, though, the same rules apply for sec as for cos. For example \cos (-\theta) = \cos \theta \implies \dfrac{1}{\cos (-\theta)} = \dfrac{1}{\cos \theta}, and so \sec (-\theta) = \sec \theta. Similarly, \sec (\theta + \pi) = -\sec \theta... and so on.
    Is it the same when its cot too?
    • PS Helper
    Offline

    14
    (Original post by Nkhan)
    Is it the same when its cot too?
    Yes, except you have to use the rules for \tan.
    • Thread Starter
    Offline

    0
    ReputationRep:
    (Original post by nuodai)
    Yes, except you have to use the rules for \tan.
    Yeap I get it now cheers
    Im just gonna use that trig quadrant thing to work em all out
 
 
 
  • 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.

  • Poll
    Did TEF Bronze Award affect your UCAS choices?
    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.