# Cos Angle problem

• January 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.

• January 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.

e) Use your calculator to solve for cosx using the original equation, but don't forget that when you do cosINV(8/17) on your calculator it'll give you the angle in the first quadrant, so you'll need to subtract that angle from 360 (in degrees) or 2pi (in radians) to get the one in the 4th quadrant.

Anyway, hope that helps!