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Terminating angles?

  1. Sep 9, 2004 #1
    terminating angles??

    If sin(x) = cos(x), in which quadrants can angle x terminate?
    I have no clue what this question is asking.

    also...

    If {x+sin(x)}/cos(x) then f(pi) = ?

    {pi+sin(pi)}/cos(pi)= pi+0/-1 = -pi

    is that correct?
     
  2. jcsd
  3. Sep 9, 2004 #2

    Gokul43201

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    1. Rephrasing : For what values of x does sin(x) = cos(x). Which quadrants are these values of x in ?

    0 to 90 (pi/2 rad) is Q1
    90 to 180 (pi rad) is Q2
    180 to 270 (3pi/2 rad) is Q3
    270 to 360 or 0 (2pi or 0 rad) is Q4

    Have you tried drawing the curves of sin(x) and cos(x) ? What happens with these curves when sin(x) = cos(x) ?

    2. Assuming you mean "If f(x) = {x+sin(x)}/cos(x) then f(pi) = ?", your answer is correct.
     
  4. Sep 9, 2004 #3
    I don't know if this will help, however, where sin(x) = cos(x), x is in the first and third quadrants.

    You may want to take a look at figure 9 here:
    http://mpec.sc.mahidol.ac.th/physmath/mat12/curve810.jpg

    EDIT: Woops! Gokul beat me to helping you.
     
    Last edited: Sep 9, 2004
  5. Sep 9, 2004 #4
    I understand, so it's quadrants I and III.

    For the second question, the question just says If {x+sin(x)}/cos(x), then f`(pi)= ?
    the choices are... (a) 2 (B) 1 (C) -1 (D) -2 (E) 0

    I got an answer of -pi which isnt any of the choices, is there a mistake in the question?
     
  6. Sep 9, 2004 #5

    Pyrrhus

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    Check again for the quadrants.

    does F'(pi) stand for first derivative evaluating pi?

    assuming it does.

    [tex] F'(x) = \frac{1+\cos(x)+x\sin(x)}{\cos^2(x)} [/tex]

    [tex] F'(pi) = 0 [/tex]

    -Cyclovenom
     
  7. Sep 9, 2004 #6
    according to recon's link, sinX=cosX in the 1st and 3rd quadrant. SinX and CosX intersect between 0 and 90 as well as between 180 and 270 which are the 1st and 3rd quadrants. What am I missing?
     
  8. Sep 10, 2004 #7

    ShawnD

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    The answer might just be hiding in plane sight (sorry, bad math joke).

    [tex]sin(x) = cos(x)[/tex]

    [tex]\frac{sin(x)}{cos(x)} = 1[/tex]

    [tex]tan(x) = 1[/tex]

    :wink:
     
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