algebra 2 high school

Question

cos q=o.53 and 270degrees<q<360 find q to the nearest thousanth 

Answer 1

q = arccos 0.53 on calculator, in degree mode, gives angle q = 58⁰, rounded, but of course that is in quadrant 1, and we must convert it to a related angle in quadrant 4.  that angle is 360 - 58 = 302^o

Answer 2

Hi Ashley,

 

cosq = 0.53

q = 57.995 degrees (rounded to the nearest thousandth)

But this is in the first quadrant. You are given that the angle is in the fourth quadrant 270<q<360, therefore

we know that cosq = cos(-q) this is a symmetric identity.

then the angle q will be 2pi - q = 360 - 57.995 = 302.005°