SOLUTION: Solve equation for all value of ø if ø measure in degrees cos2ø+3cosø -1=0

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Question 403218: Solve equation for all value of ø if ø measure in degrees
cos2ø+3cosø -1=0
Answer by Tatiana_Stebko(1539) About Me  (Show Source):
You can put this solution on YOUR website!
cos2w%2B3cosw+-1=0
Use FORMULA cos2w=%28cosw%29%5E2-%28sinw%29%5E2
cos2w%2B3cosw+-1=0
%28cosw%29%5E2-%28sinw%29%5E2%2B3cosw-1=0
Use FORMULA %28sinw%29%5E2=1-%28cosw%29%5E2
%28cosw%29%5E2-%281-%28cosw%29%5E2%29%2B3cosw-1=0
%28cosw%29%5E2-1%2B%28cosw%29%5E2%2B3cosw-1=0
2%28cosw%29%5E2%2B3cosw-2=0
Let cosw=t, -1%3C=t%3C=1
2t%5E2%2B3t-2=0
t+=+%28-3+%2B-+sqrt%28+3%5E2-4%2A2%2A%28-2%29%29%29%2F%282%2A2%29+
t+=+%28-3+%2B-+sqrt%28+25%29%29%2F4+
t+=+%28-3+%2B5%29%2F4+ or t+=+%28-3+-5%29%2F4+
t+=+1%2F2+ or t+=+-2+>1
t+=+1%2F2+ , so cosw=1%2F2,
Use FORMULA if cosw=a, then w=+-arccos(a)+360k, k is any integer
cosw=1%2F2
w=+-arccos(1/2)+360k
w=+-60+360k, k is any integer