Question 978444: Solve, finding all solutions in [0,π)
2cosx+1=2.6931
I know the answer is: 0.5613,5.7219 but why? Could you show me how to solve it step by step please?
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website! Did you mean [0, 2pi) instead of [0,pi) ?
I'm going to assume that is the case. Anyways, solve for x to get
2*cos(x) + 1 = 2.6931
2*cos(x) = 2.6931 - 1
2*cos(x) = 1.6931
cos(x) = 1.6931/2
cos(x) = 0.84655
x = arccos(0.84655)+2pi*n or x = -arccos(0.84655)+2pi*n
x = 0.5613+2pi*n or x = -0.5613+2pi*n
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The general form of the solutions is
x = 0.5613+2pi*n or x = -0.5613+2pi*n
where n is an integer (ie a whole number). You replace n with an integer to get a particular solution.
If you plug in n = 0 and n = 1, you'll get x = 0.5613 and x = 5.7219 respectively. Both are approximate. Any other value of n will produce values that are outside of the interval [0, 2pi)
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