Posted by Kelly on Monday, March 14, 2011 at 6:38pm.
Is this cosx=1/2sqrt3 ?
no it's 2cosx-sqrt3=0
I will read it as
2cosx - √3 = 0
cosx = √3/2
x = 30 , from the standard 30-60-90 triangle
or x = 330
"all solutions " would be
x = 30 + k(360) or x = 330+k(360) where k is an integer.
How do you find the solutions?
since the standard cosine curve has a period of 360, any answer you have will repeat itself in the next curve or 360 either to the right or to the left.
by multiplying 360 by k, k and integer, I am simply adding/or subtracting multiples of 360 to any answer.
to get my original 30, as I said, I recognized the rations of the 30-60-90 right-angled triangle, which are 1:√3:2.
Secondly , since the cosine is positive in the 1st and 4th quadrant, the 30 will be the 1st quadrant solution and 360-30 or 330 would be the 4th quadrant solution.
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