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

**gateway** · Aug 3rd 2008, 07:46 AM

**wingless** · Aug 3rd 2008, 07:57 AM

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.

**nikhil** · Aug 3rd 2008, 08:10 AM

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

**wingless** · Aug 3rd 2008, 08:34 AM

True, I counted the quadrants clockwise

**masters** · Aug 3rd 2008, 10:58 AM

Originally Posted by gateway

$\sin x=\frac{5}{13} \ \ \tan x=-\frac{5}{12} \ \ x=?$

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.

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

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

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

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

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