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Graphing calc help

  1. May 22, 2005 #1
    how do u type cos^2 x = 2 into a graphing calc because when ever use push cos it puts the ( so u cant a ^2 before it.
  2. jcsd
  3. May 22, 2005 #2
    Do you know what a function squared means? It means the function times itself..
  4. May 22, 2005 #3
    ya i know, but i just want to know how to solve cos^2 x = 2 but i dont know how
  5. May 22, 2005 #4


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    Staff Emeritus
    Science Advisor

    Unfortunately your calculator isn't going to think for you.

    The direct way (what I would consider the "mathematical" way) is to solve the equation yourself then use your calculator to get the number.

    You have cos2x= 2. That means two things have been done to x: take the cosine and then square. To solve the equation, you have to 'back out'- do the opposite of what has been done: the opposite of squareing is square root- from
    cos2x= 2 you get [tex]cos(x)= \sqrt{2}[/tex]. BUT you also have to know that a negative number, squared, is a positive number [tex]cos x= -\sqrt{2}[/tex] is also a possibility. Now, the "inverse" of cosine in arccos or cos-1 so from [tex]cos x= \sqrt{2}[/tex] you get [tex]x= cos^{-1}(\sqrt{x}): but, again, there are many solutions to the equation. If you have really learned these functions, you could work out a formula for all solutions.

    Another way to use a graphing calculator to solve an equation like this is to graph two functions: y= cos2 x and y= 2. The "zoom" into the places where the two graphs cross. Of course, that wont give you a formula that enables you to writed down all solutions but it might let you pass the course without actually having to learn any mathematics!
  6. May 22, 2005 #5
    Its a shame the overuse of calculators. I remember in high school people who would reach for their calculator when asked for the answer to 12+9.
  7. May 22, 2005 #6
    im sry if you think im not trying but im not taking a trig course im just in algebra 2 and my teacher wanted to touch on trig.
    But with the calc you said to type in y= cos^2 x but i dont know to do that with my ti 83+ because when i push the cos button in outputs cos( so i cant put a ^2
  8. May 22, 2005 #7
    I already told you how to solve this problem.

    Hit the y-function button on the top left. Then in the first line press the cos button, in parenthesis enter x, and close the parentheses. Then put ^2 outside.
    Alternatively you could enter cos(x)*cos(x) , which equals cos^2(x) = cos(x)^2
  9. May 22, 2005 #8
    but i thought

    cos(x)^2 doesnt equal cos^2 (x)
  10. May 22, 2005 #9
    [tex] cos^2(x) = cos(x)^2 = cos(x)cos(x) \neq cos(x^2) [/tex]
  11. May 22, 2005 #10
    ok thxs

    so i want to solve this for x over [tex][-2pi, 2pi][/tex]
    [tex] cot(x)cos^2(x) = 2 cot(x) [/tex]

    [tex] cos^2(x) = 2 [/tex]

    [tex]x= cos^{-1}(\sqrt{2}): [/tex]

    but how do i find all of the solution i am looking for from there
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