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Reciprocal of cos?

  1. Nov 29, 2015 #1
    Why 1 divided by cos(pi/4)=cos(-pi/4)?
    Is it wrong to say 1/cos(pi/4)=sec(pi/4)?

  2. jcsd
  3. Nov 29, 2015 #2

    Buzz Bloom

    User Avatar
    Gold Member

    Hi ryan:

    Is it wrong to say 1/cos(pi/4)=sec(pi/4)?​
    1/cos(pi/4)=sec(pi/4) is correct.

    Why 1 divided by cos(pi/4)=cos(-pi/4)?​
    I think you are asking: Why is the following correct?
    1/cos(pi/4) = 1/cos(-pi/4)?​
    If this is what you are asking, the reason that is correct is because
    cos(pi/4) = cos(-pi/4),​
    which is because
    the cos function is symmetrical,​
    and because
    the reciprocal of two equal numbers will be equal.​

    I hope this is helpful.

    BTW: The title of the thread does not match your question. The inverse of the cos is the arccos, which is not the same as the reciprocal, 1/cos.

    Last edited: Nov 29, 2015
  4. Nov 29, 2015 #3
    Thanks you
  5. Nov 29, 2015 #4


    Staff: Mentor

    The thread title is now "Reciprocal of cos".
  6. Dec 1, 2015 #5

    1/cos(pi/4) is not equal to cos(-pi/4). Cos(-pi/4) is equal to cos(pi/4). It is because cos function is an even function and it produces same answer to negative and positive values. I can give you a simple reason that 0 and 2pi is same in angles and 0-pi/4 is same as 2pi-pi/4 if you see graph paper, rotate a line from positive X-axis in anti-clock wise direction it lies in fourth quadrant. Now, you see x co-ordinate is positive and hypotenuse is length so it's positive. Hence, base/hypotenuse is positive.

    I hope this one helps and if any other query regarding my answer please ask.
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