1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Trig Typo?

  1. Oct 31, 2008 #1
    b]1. The problem statement, all variables and given/known data[/b]
    Hey, I have a problem that I worked out in a trigonometry book. I got different answers from what the book gave, but I think that I am right and the book is wrong. Could someone please tell me who is right?

    2. Relevant equations

    Okay, they gave me the following problem: solve for x in secx^2-4=0 when 0 is less than or equal to x, which is less than or equal to 360.

    Here is how the book solves it:

    secx-2=0 secx+2=0
    secx=2 secx=-2
    x=sec^-1(2) x=sec^-1(-2)
    = 30, 330 = 150, 210

    Okay, here's where I have a big problem: secant is the reciprocal function of cosine, right?
    So if we evaluate x=sec^-1(2), we get cos^-1(1/2), which does not equal 30 and 330 when plugged into the calculator. Same situation with x=sec^-1(-2).
    I am pretty sure that this is a horrible typo, but I would be delighted to be corrected otherwise.

    3. The attempt at a solution
    1. The problem statement, all variables and given/known data

    2. Relevant equations

    3. The attempt at a solution
  2. jcsd
  3. Oct 31, 2008 #2
    I agree with you. If you want places where cos(x) = +/-.5 then that is 60,120,240,300. Also I graphed [sec(x)]^2-4 and it was 0 at those places. The values they gave were correct for sine. So unless the original problem is [csc(x)]^2-4=0, their answer is wrong.
  4. Oct 31, 2008 #3


    User Avatar
    Science Advisor
    Gold Member

    Actually sec x = 1/cos x. I think you are confusing ^-1 and inverse functions.
  5. Oct 31, 2008 #4
    I think that there is a typo, the answers should actually be x = 60, 120, 240, 300.

    Solution from where the book leaves off:
    sec(x) = 2, sec(x) = -2
    1/2 = cos(x), -1/2 = cos(x)
    Use graph or calculator to find the angles are those that I stated above.
  6. Nov 1, 2008 #5


    User Avatar
    Science Advisor

    No, he said "reciprocal", not "inverse". There is NO cos-1(2).
  7. Nov 1, 2008 #6


    User Avatar
    Science Advisor
    Gold Member

    Oops. Sorry.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Similar Discussions: Trig Typo?
  1. Trig Asymptotes (Replies: 3)

  2. Trig question (Replies: 2)

  3. Trig Identities (Replies: 18)

  4. Trig Proof (Replies: 4)

  5. Trig equation (Replies: 10)