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Thread: sin x=5/13 tan x=-5/12 ;x=?

  1. #1
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    sin x=5/13 tan x=-5/12 ;x=?

    sin x=5/13 tan x=-5/12 ;x=?
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  2. #2
    Super Member wingless's Avatar
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    Hint:
    If sin x is positive, then x can be in the 1st and 4th quadrants. If tan x is negative, x can be in the 2nd and 4th quadrants.
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  3. #3
    Senior Member nikhil's Avatar
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    Quote Originally Posted by wingless View Post
    Hint:
    If sin x is positive, then x can be in the 1st and 4th quadrants. If tan x is negative, x can be in the 2nd and 4th quadrants.
    correction
    sin x is positive, then x can be in the 1st and 2nd quadrants
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  4. #4
    Super Member wingless's Avatar
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    True, I counted the quadrants clockwise
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  5. #5
    A riddle wrapped in an enigma
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    Quote Originally Posted by gateway View Post
    $\displaystyle \sin x=\frac{5}{13} \ \ \tan x=-\frac{5}{12} \ \ x=?$
    You're looking for an angle whose terminal side is in the second quadrant, since that's the quadrant where Sin is positive and Tan is negative.

    $\displaystyle \theta=\arcsin\left(\frac{5}{13}\right)\approx22.6 ^\circ$

    The reference angle in the 2nd quadrant is $\displaystyle 22.6^\circ$

    For any angle $\displaystyle \theta, \ \ 0 < \theta < 180^\circ$, its reference angle is defined as $\displaystyle 180^\circ - \theta$

    $\displaystyle \theta = 180^\circ - 22.6^\circ \approx 157.4^\circ$
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