SOLUTION: Hi, I am having difficulty with the problem: sec theta + 10 = 2 - 4 sec theta I tried combining like terms and came up with sec theta= -8/5 but i feel that is incorrect. Any help

Question 928048: Hi, I am having difficulty with the problem:
sec theta + 10 = 2 - 4 sec theta
I tried combining like terms and came up with sec theta= -8/5 but i feel that is incorrect. Any help would be greatly appreciated, thank you in advance!
Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
sec theta + 10 = 2 - 4 sec theta
sec(theta) + 4sec(theta) = -8
1/cos(theta) +4/cos(theta) = -8
5/cos(theta) = -8/1
cross multiply fractions
-8cos(theta) = 5
cos(theta) = -5/8 or sec(theta) = -8/5
if you are looking for a value for theta then
inverse cos(theta) = 2.24592786 radians, assuming -5/8 is radians
theta in degrees = (180*2.24592786) / pi = 128.682187452 approx 129 degrees

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