Results 1 to 5 of 5

Math Help - Using Trigonometric Identities

  1. #1
    Senior Member vaironxxrd's Avatar
    Joined
    Nov 2010
    From
    USA
    Posts
    424
    Thanks
    1
    Awards
    1

    Using Trigonometric Identities

    Hello Everyone,

    I have the following instruction, "Use trigonometric identities to transform one side of the equation into the other" ?

    First I don't exactly understand what the instructions are saying.


    The problem is as follows

    cos Θ sec Θ = 1

    The book gives me the solution which is

    cos Θ sec Θ = 1 \frac{1}{sec Θ} = 1

    ( 0 < Θ < π/2) (I guess this means Θ is an acute angle)
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,605
    Thanks
    1573
    Awards
    1

    Re: Using Trigonometric Identities

    Quote Originally Posted by vaironxxrd View Post
    I have the following instruction, "Use trigonometric identities to transform one side of the equation into the other" ? First I don't exactly understand what the instructions are saying. The problem is as follows
    cos Θ sec Θ = 1
    The book gives me the solution which is
    cos Θ sec Θ = 1 \frac{1}{sec Θ} = 1
    ( 0 < Θ < π/2) (I guess this means Θ is an acute angle)

    If the question is to solve for \theta in the equation \cos(\theta)\sec(\theta)=1 then the answer given makes no sense.
    Because the solution is \forall\theta\left[\theta\ne\frac{(2n+1)\pi}{2}\right].

    On the other hand, did the statement begin with restrictions on \theta~?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Senior Member vaironxxrd's Avatar
    Joined
    Nov 2010
    From
    USA
    Posts
    424
    Thanks
    1
    Awards
    1

    Re: Using Trigonometric Identities

    Quote Originally Posted by Plato View Post
    If the question is to solve for \theta in the equation \cos(\theta)\sec(\theta)=1 then the answer given makes no sense.
    Because the solution is \forall\theta\left[\theta\ne\frac{(2n+1)\pi}{2}\right].

    On the other hand, did the statement begin with restrictions on \theta~?
    The book first gives the instruction, "transform one side of the equation into the other" (Which doesn't make any sense to me)
    It also doesn't provide any specific angle it just states the following ( 0 < \theta < \pi/2)

    The actual problem to be solved is...
    cos \theta sec \theta = 1

    The solution is...
    "Simplify the expression on the left-hand side of the equation until you obtain the right side"
    cos\theta sec\theta = \frac{1}{sec\theta}\cdot sec\theta = 1
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,605
    Thanks
    1573
    Awards
    1

    Re: Using Trigonometric Identities

    Quote Originally Posted by vaironxxrd View Post
    The book first gives the instruction, "transform one side of the equation into the other" (Which doesn't make any sense to me)
    It also doesn't provide any specific angle it just states the following ( 0 < \theta < \pi/2)

    The actual problem to be solved is...
    cos \theta sec \theta = 1

    The solution is...
    "Simplify the expression on the left-hand side of the equation until you obtain the right side"
    cos\theta sec\theta = \frac{1}{sec(\theta})\cdot sec\theta = 1


    Well your reply confuses me.

    It is absolutely true that if 0<\theta<\frac{\pi}{2} then \cos(\theta)\sec(\theta)=1.

    So what is the big deal?
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Senior Member vaironxxrd's Avatar
    Joined
    Nov 2010
    From
    USA
    Posts
    424
    Thanks
    1
    Awards
    1

    Re: Using Trigonometric Identities

    Quote Originally Posted by Plato View Post
    Well your reply confuses me.

    It is absolutely true that if 0<\theta<\frac{\pi}{2} then \cos(\theta)\sec(\theta)=1.

    So what is the big deal?

    All the instructions given are to "Use trigonometric identities to transform one side of the equation into the other".
    I myself am confused on where to start
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Trigonometric Identities
    Posted in the Trigonometry Forum
    Replies: 4
    Last Post: August 10th 2011, 11:22 AM
  2. Trigonometric Identities
    Posted in the Trigonometry Forum
    Replies: 7
    Last Post: June 4th 2011, 10:08 PM
  3. trigonometric identities
    Posted in the Trigonometry Forum
    Replies: 11
    Last Post: September 14th 2008, 11:49 AM
  4. Trigonometric Identities
    Posted in the Trigonometry Forum
    Replies: 1
    Last Post: September 13th 2008, 11:32 AM
  5. trigonometric identities
    Posted in the Trigonometry Forum
    Replies: 3
    Last Post: May 8th 2007, 04:41 AM

Search Tags


/mathhelpforum @mathhelpforum