# Cos Angle problem

• Jan 21st 2009, 04:49 PM
Random-Hero-
Cos Angle problem
It's the last dang question and I can't quite seem to wrap my head around it. >: (

The angle 2x lies in the fourth quadrant such that cos 2x = 8/17

a) Sketch the location of angle 2x.

b) Which Quadrant contains angle x?

c) Determine an exact value for cos x.

d) Use a calculator to determine the measure of x, in radians.

• Jan 21st 2009, 08:41 PM
JD-Styles
a) I can't really sketch but I'll try explaining it: 8/17 is a little less than 1/2, and since it's in the fourth quadrant, 2x must be just a little less than 300 degrees.

b) If 2x is a little less than 300, but it's certainly bigger than 270 (indeed cos270=0) so 270<2x<300, which implies 135<x<150, meaning x is in the second quadrant.

c) Here you'd use the identity for cos(2x):

$
cos(2x)=\frac{8}{17}
$

$
2cos^2x-1=\frac{8}{17}
$

$
cosx=-\sqrt{\frac{25}{34}}
$

N.B. we only take the negative root because the positive one would give us an angle in the first or 4th quadrants. Check it and see.