SOLUTION: Solve equation for all value of ø if ø measure in degrees 2cos^2ø+2=5cosø

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Question 399928: Solve equation for all value of ø if ø measure in degrees
2cos^2ø+2=5cosø

Answer by Tatiana_Stebko(1539) About Me  (Show Source):
You can put this solution on YOUR website!
2%28cosw%29%5E2%2B2=5cosw
2%28cosw%29%5E2-5cosw%2B2=0
make the substitution x=cosw, x have to be from the interval [-1;1](because cosw always takes values only in the interval[-1;1])
2x%5E2-5x%2B2=0
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
x+=+%28-%28-5%29+%2B+sqrt%28+%28-5%29%5E2-4%2A2%2A2+%29%29%2F%282%2A2%29+ or x+=+%28-%28-5%29+-+sqrt%28+%28-5%29%5E2-4%2A2%2A2+%29%29%2F%282%2A2%29+
x+=+%285+%2B+sqrt%28+9%29%29%2F4+ or x+=+%285+-+sqrt%28+9%29%29%2F4+
x+=+2 or x+=+1%2F2
x+=+2 is extraneous root of the equation because it does not belong to the interval [-1;1]
So x+=+1%2F2,
make the substitution back x=cosw, cosw=1%2F2
FORMULA: the solution of eguation cosw=a is w=+-arccos%28a%29%2B360%2Ak k is any integer
w=+-arccos%281%2F2%29%2B360%2Ak k is any integer
w=+-60%2B360%2Ak k is any integer