SOLUTION: Why do cos(1043π) cos(164π) cos(163π) all equal -1 I can do the calculation up to cos(1043) -> 1043-1 -> 1042/2 -> 521*2π+π but where does the

Algebra ->  Trigonometry-basics -> SOLUTION: Why do cos(1043π) cos(164π) cos(163π) all equal -1 I can do the calculation up to cos(1043) -> 1043-1 -> 1042/2 -> 521*2π+π but where does the       Log On


   

Question 923354: Why do
cos(1043π)
cos(164π)
cos(163π)
all equal -1
I can do the calculation up to cos(1043) -> 1043-1 -> 1042/2 -> 521*2π+π but where does the -1 come from?
Thank you
Found 2 solutions by ewatrrr, lwsshak3:
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
 

Hi,

(cosx, sinx) Summary Unit Circle

.

cos(1043π) = cos(π + 1042π) = cos(π) = -1

.....

cos(163π) = cos(π + 162π) = cos(π) = -1

.....

cos(164π) = cos(0 + 164π) = cos(0) = 1

Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
Why do
cos(1043π)
rotate cc 1042π + π which becoms the reference angle in quadrant I
cos(1043π)=cosπ=-1
..
cos(164π)
rotate cc 164π, which terminates at 0, which becomes the reference angle
cos(164π)=cos 0=1 (contrary to your statement)
..
cos(163π)
rotate cc 162π + π which becoms the reference angle
cos(163π)=cosπ=-1
Note: even number of π's terminate at 0; whereas, odd number of π's terminate at π