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Math Help - Trig equation

  1. #1
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    Trig equation

    Hi
    Can anyone tell me how to do this:

    If cosecant A=3.168 find secant A

    -I understand that secant=1/cos and that cosecant is 1/sin but I am still confused
    Thanks a lot to anyone who took the time to read this!
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by stephie View Post
    Hi
    Can anyone tell me how to do this:

    If cosecant A=3.168 find secant A

    -I understand that secant=1/cos and that cosecant is 1/sin but I am still confused
    Thanks a lot to anyone who took the time to read this!
    ok, so you know the relationships, so use them. here's how

    i will use csc for cosecant and sec for secant

    cscA = 3.168
    => 1/sinA = 3.168
    => sinA = 1/3.168 = 0.316
    now we know that sin^2(A) + cos^2(A) = 1
    we know the value of sinA so let's plug it in to find cosA

    => (0.316)^2 + cos^2(A) = 1
    => cos^2A = 1 - (0.316)^2 = 0.9
    => cosA = 0.949

    so cosA = 0.949
    => 1/cosA = 1/0.949 = 1.054
    => secA = 1.054....

    i rounded off some stuff while doing this problem, if you want a more accurate answer you can redo this with more decimal places
    Last edited by Jhevon; April 10th 2007 at 12:02 PM.
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  3. #3
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    thank you
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  4. #4
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    Hello, stephie!

    If csc A = 3.168, find sec A.
    . . . . . . . . . . . . . . . - . . . . . . . . . . __
    That decimal looks suspiciously like √10.
    . . . . . . . . . . . . . . . . __
    . . . . . . . . . . . . . . . √10 . - . hyp
    We have: . csc A .= .------ .= .-----
    . . . . . . . . . . . . . . . . 1 . - . . opp

    . . . . . . . . . . . . . . . . . . . . . . . . - . . . - . . . . . . . . __
    Hence, A is an angle in a right triangle with: .hyp = √10 and opp = 1.


    Using Pythagorus, we find that: .adj = 3

    . . . . . . . . . . . . . . . . . . . . . . .__
    . . . . . . . . . . . . . . . .hyp . . . √10
    Therefore: . sec A .= .----- .= .-----
    . . . . . . . . . . . . . - . .adj . . . . .3

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  5. #5
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by Soroban View Post
    Hello, stephie!

    . . . . . . . . . . . . . . . - . . . . . . . . . . __
    That decimal looks suspiciously like √10.
    . . . . . . . . . . . . . . . . __
    . . . . . . . . . . . . . . . √10 . - . hyp
    We have: . csc A .= .------ .= .-----
    . . . . . . . . . . . . . . . . 1 . - . . opp

    . . . . . . . . . . . . . . . . . . . . . . . . - . . . - . . . . . . . . __
    Hence, A is an angle in a right triangle with: .hyp = √10 and opp = 1.


    Using Pythagorus, we find that: .adj = 3

    . . . . . . . . . . . . . . . . . . . . . . .__
    . . . . . . . . . . . . . . . .hyp . . . √10
    Therefore: . sec A .= .----- .= .-----
    . . . . . . . . . . . . . - . .adj . . . . .3

    well, 3.168 is a bit bigger than sqrt(10), but i guess that will suffice. your way is a much nicer way to do the problem i would have done it that way if they gave us a whole number or fraction
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