# Finding value of x

• Aug 14th 2011, 03:17 PM
benny92000
Finding value of x
What is the value of x if 180 < x < 270. (less than OR equal to 270, greater than OR equal to 180) and sinx = 5cosx.

Ok, I graphed both of these and searched for point of intersection.. The answer is 4.515. I'm a bit confused. I thought that the limits would put the answer in quadrant 3. Why, then, is the solution positive x?
• Aug 14th 2011, 03:51 PM
skeeter
Re: Finding value of x
Quote:

Originally Posted by benny92000
What is the value of x if 180 < x < 270. (less than OR equal to 270, greater than OR equal to 180) and sinx = 5cosx.

Ok, I graphed both of these and searched for point of intersection.. The answer is 4.515. I'm a bit confused. I thought that the limits would put the answer in quadrant 3. Why, then, is the solution positive x?

$\displaystyle \sin{x} = 5\cos{x}$

$\displaystyle \frac{\sin{x}}{\cos{x}} = 5$

$\displaystyle \tan{x} = 5$

since $\displaystyle 180 < x < 270$

$\displaystyle x = \arctan(5) + 180$

tangent is positive in quad III