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Tan x-intercepts

  1. Aug 7, 2005 #1
    the tan graph is in the form y=atan(b(x-c))+d how do you determine the "EXACT" x-intercept of this graph in radian form when the d value does not equal 0 and is there a formula for finding the x-intercept when given the equation in the form above using the values of a,b,c and d which control the vertical/horizontal stretch/shift
     
    Last edited: Aug 7, 2005
  2. jcsd
  3. Aug 7, 2005 #2
    same way you get the zeros for any function: let y=0.
     
  4. Aug 7, 2005 #3
    whoops i need to edit it i mean as an exact value in radian form like pi/2 for example
     
  5. Aug 7, 2005 #4
    well, in general, your answer is just going to have to be left in terms of arctangents, multiplied by some factor and then added to by another factor.

    neat answers like pi/2 only come up only in special situations, unfortunately!
     
  6. Aug 7, 2005 #5
    and my mom is NOT 98! :mad:




    :tongue:
     
  7. Aug 8, 2005 #6
    okay so there are not going to be neat answers so is my only way to get a estimated answer in radian to graph it using a calculator and then trace the zeros? or is there a way to determine it without graphing?
     
  8. Aug 8, 2005 #7

    jtbell

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    Staff: Mentor

    You need to take the equation

    [tex]\arctan (b (x - c)) + d = 0[/tex]

    and solve it for [itex]x[/itex], that is, rearrange it into the form

    [tex]x = something[/tex]

    Then plug in whatever values you have for [itex]b[/itex], [itex]c[/itex], and [itex]d[/itex]. Where do you get stuck when you try to do this?
     
  9. Aug 8, 2005 #8
    that wasn't his equation.

    it was a*tan(b(x-c) + d.

    "a" is a stretching/shrinking factor. (i guess it's that there are only two missing letters between atan and arctan and the fact that i mentioned arctan that led you to this.)
     
  10. Aug 8, 2005 #9
    some simple algebra says: [tex]x=\frac{\tan^{-1}(-\frac{d}{a})}{b}+c[/tex]
     
    Last edited: Aug 8, 2005
  11. Aug 8, 2005 #10
    "+c," right?
     
  12. Aug 8, 2005 #11

    jtbell

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    Staff: Mentor

    Oops. I've done too much computer programming in languages that call the arctangent function "atan". :blushing:
     
  13. Aug 8, 2005 #12
    yea it +c not -c so this gets me the so therefore i can now just like add or substract another period to this answer to get another x-intercept rite?

    thx everyone :smile:
     
  14. Aug 8, 2005 #13
    yea, oops. maybe i should proofread before i submit
     
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