sin x=5/13 tan x=-5/12 ;x=? (Headbang)(Headbang)(Headbang)

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- Aug 3rd 2008, 07:46 AMgatewaysin x=5/13 tan x=-5/12 ;x=?
sin x=5/13 tan x=-5/12 ;x=? (Headbang)(Headbang)(Headbang)

- Aug 3rd 2008, 07:57 AMwingless
**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. - Aug 3rd 2008, 08:10 AMnikhil
- Aug 3rd 2008, 08:34 AMwingless
True, I counted the quadrants clockwise (Itwasntme)

- Aug 3rd 2008, 10:58 AMmasters
You're looking for an angle whose terminal side is in the second quadrant, since that's the quadrant where

is positive and*Sin*is negative.*Tan*

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

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 $\displaystyle 180^\circ - \theta$

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