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Homework Help: Find the exact value

  1. Jun 26, 2008 #1
    1. The problem statement, all variables and given/known data
    Find the exact value of the function:
    tan(cos^-1 0.5)


    2. Relevant equations

    I used this formula: y=sin^-1=sin y=x for the first part, how do I solve the second part of the problem tanx (x)?

    3. The attempt at a solution
    x=cos^-1 (0.5)
    cos(N)=0.5
    N= pi/3
    Then I tried tanx(x)=
    I'm stuck
     
  2. jcsd
  3. Jun 26, 2008 #2

    D H

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    Why did you change x to N?
     
  4. Jun 26, 2008 #3
    [tex]\tan{(\cos^{-1}\frac 1 2)}=\tan x[/tex]

    [tex]x=\cos^{-1}\frac 1 2[/tex]

    [tex]x=\frac{\pi}{3}[/tex]

    Ok, you have x? So your equation just ... [tex]\tan x[/tex] ... solve for tangent!
     
  5. Jun 26, 2008 #4
    Don't know? good question, but I see that I just have to plug in pi/3 into tanx (x)
     
  6. Jun 27, 2008 #5

    HallsofIvy

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    [tex]tan(x)= tan(\pi/3)= \frac{sin(\pi/3)}{cos(\pi/3)}[/itex]
    Surely you know [itex]sin(\pi/3)[/itex] and [itex]cos(\pi/3)[/itex]!
     
    Last edited by a moderator: Jun 27, 2008
  7. Jun 27, 2008 #6
    The first line of ivy should be:
    [tex]tan(x)= tan(\pi/3)= \frac{sin(\pi/3)}{cos(\pi/3)}[/itex]
     
  8. Jun 27, 2008 #7

    Dick

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    There's another way to do this. Draw a right triangle that has a angle of cos^(-1)(1/2) in it. E.g. hypotenuse 1 and adjacent side 1/2. Use Pythagoras to find the missing side. Now find tan by opposite/adjacent.
     
  9. Jun 27, 2008 #8
    Thank you!
     
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