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Math Help - Exact value of tan (x)

  1. #1
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    Exact value of tan (x)

    If sec (x) = -4/3 and sin (x) > 0, find the exact value of tan (x)...
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  2. #2
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    Sec and tan

    Hi tradar -

    Quote Originally Posted by tradar View Post
    If sec (x) = -4/3 and sin (x) > 0, find the exact value of tan (x)...
    First you need to use:

    \sec^2 x = 1 + \tan^2 x

    This will give you a value for \tan^2 x. When you take the square root, be careful with the \pm sign. Which do you choose?

    Well, we're told that \sin x > 0 and \sec x < 0. Now \cos x = \frac{1}{\sec x}. So \cos x < 0. And, of course, \tan x = \frac{\sin x}{\cos x}, so \tan x < 0 also.

    So take the negative square root, and there's your answer.

    Grandad
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