SOLUTION: solve the equation for the solution over the interval [0,360) tan^2theta+ 4sec theta=-5 finals tomorrow and have no idea thanks so much and god bless

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Question 743902: solve the equation for the solution over the interval [0,360)
tan^2theta+ 4sec theta=-5
finals tomorrow and have no idea thanks so much and god bless
Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
tan^2theta+ 4sec theta=-5
sin%5E2%28x%29%2Fcos%5E2%28x%29%2B4sec%28x%29=-5
sin%5E2%28x%29%2Fcos%5E2%28x%29%2B4%2Fcos%28x%29%2B5=0
LCD:cos^2(x)
sin%5E2%28x%29%2B4cos%28x%29%2B5cos%5E2%28x%29=0
1-cos%5E2%28x%29%2B4cos%28x%29%2B5cos%5E2%28x%29=0
4cos%5E2%28x%29%2B4cos%28x%29%2B1=0
solve for cos(x) by quadratic formula
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
a=4, b=4, c=1
cos%28x%29=%28-4%2B-sqrt%2816-16%29%29%2F%288%29=%28-4%2B-sqrt%280%29%29%2F8=-1%2F2
x=120º, 240º ( in Q2 and Q3 where cos<0)