SOLUTION: Find all solutions in the interval [0,2pi) Cos^2 theta -9 cos theta - 1 =0 (Type your answer in radians. Round to four decimal places as needed. Use a comma to separate answers

Question 1197838: Find all solutions in the interval [0,2pi)
Cos^2 theta -9 cos theta - 1 =0
(Type your answer in radians. Round to four decimal places as needed. Use a comma to separate answers as needed.)
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
Find all solutions in the interval [0,2pi)
Cos^2 theta -9 cos theta - 1 =0
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If you mean Cos^2(t) -9cos(t) - 1 = 0
Sub x for cos(t)

Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)

Quadratic equation (in our case ) has the following solutons:

For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=85 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 9.10977222864644, -0.109772228646444. Here's your graph:

===============
Ignore the value >1, no real solution.
cos(t) =~ -0.109772228
theta = ~96.3022 degs
theta = ~263.6978 dega
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Convert to radians if you like.
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