Question 455472
Find, to the nearest degree all of the values of x.. 2 cos^2 x + 2 sin x - 1 = 0
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2 cos^2 x + 2 sin x - 1 = 0
use following quadratic formula to solve for cos x:
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{{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}
..
a=2, b=2, c=-1
cos x=[-2±sqrt(2^2-4*2*-1)]2*2
cos x=(-2±√12)/4)
cos x=(-2±2√3)/4
cos x=-1/2±√3/2
cos x=-1/2-&#8730;3)/2=-1.366 (reject,(-1 < cos x < 1))
or
cos x=-1/2+&#8730;3)/2=.366
x=69º+2&#960;n, 291º+2&#960;n (n= any integer)