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Math Help - find cos (A) and tan (A)

  1. #1
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    find cos (A) and tan (A)

    hi all,
    i have problem with this subject..
    Given that sin (A)=-1/2, find the value of find cos (A) and tan (A)??

    thanks...
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  2. #2
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    Quote Originally Posted by pencil09 View Post
    hi all,
    i have problem with this subject..
    Given that sin (A)=-1/2, find the value of find cos (A) and tan (A)??

    thanks...
    I assume you're familiar with the following basic formulas of trigonometry:
    cos²x + sin²x = 1
    tan x = sin x / cos x

    So, if you know that sin (A) = -1/2, you get
    cos²A + (-1/2)² = 1 <=> cos²A = 1 - 1/4 <=> cos²A = 3/4
    cos A = ± sqrt(3)/2
    Whether cos A is positive or negative depends on the quadrant that the angle A is in.

    Once you know that sin A = -1/2 and cos A = ± sqrt(3)/2 , you can calculate tan A by applying the second formula:
    tan A = (-1/2)/(± sqrt(3)/2) so tan A = ±(1/sqrt(3)) , again depending on the quadrant.

    This is my first post on these forums, but I hope I was able to help.
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  3. #3
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    Quote Originally Posted by Koaske View Post
    I assume you're familiar with the following basic formulas of trigonometry:
    cos²x + sin²x = 1
    tan x = sin x / cos x

    So, if you know that sin (A) = -1/2, you get
    cos²A + (-1/2)² = 1 <=> cos²A = 1 - 1/4 <=> cos²A = 3/4
    cos A = ± sqrt(3)/2
    Whether cos A is positive or negative depends on the quadrant that the angle A is in.

    Once you know that sin A = -1/2 and cos A = ± sqrt(3)/2 , you can calculate tan A by applying the second formula:
    tan A = (-1/2)/(± sqrt(3)/2) so tan A = ±(1/sqrt(3)) , again depending on the quadrant.

    This is my first post on these forums, but I hope I was able to help.
    Thanks for the reply,
    depending on the quadrant...

    which mean there are more than 1 answer in this case....
    The two quadrant that involve are Q-3 and Q-4, because in that quadrant the value for sin A is negative, is it true??

    so the answer can like this,
    in Q-3 (quadrant 3, pi/2<A<3pi/2),
    cos A = - sqrt(3)/2 and tan A= (1/sqrt(3))
    in Q-4,
    cos A = sqrt(3)/2 and tan A= -(1/sqrt(3))

    is it true???
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  4. #4
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    Quote Originally Posted by pencil09 View Post

    so the answer can like this,
    in Q-3 (quadrant 3, pi/2<A<3pi/2),
    cos A = - sqrt(3)/2 and tan A= (1/sqrt(3))
    in Q-4,
    cos A = sqrt(3)/2 and tan A= -(1/sqrt(3))

    is it true???
    Yep I think you got it!
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