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

• Aug 3rd 2008, 07:46 AM
gateway
sin x=5/13 tan x=-5/12 ;x=?
• Aug 3rd 2008, 07:57 AM
wingless
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 AM
nikhil
Quote:

Originally Posted by wingless
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
• Aug 3rd 2008, 08:34 AM
wingless
True, I counted the quadrants clockwise (Itwasntme)
• Aug 3rd 2008, 10:58 AM
masters
Quote:

Originally Posted by gateway
$\displaystyle \sin x=\frac{5}{13} \ \ \tan x=-\frac{5}{12} \ \ x=?$ (Headbang)(Headbang)(Headbang)

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 $\displaystyle 180^\circ - \theta$

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