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April 23rd, 2009, 10:30 AM   #1
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Trig Interval Question

I solved each problem, so if someone can check them I would appreciate it!

1. Solve the equation in the interval [0,2pi)
I found all solutions of the equation to be
Cos: pi/2 +2npi ; 3pi/2 + 2npi The problem is both yield error when plugging into a calc so do I just exclude? n is any integer
Tan: pi/4 +npi (this is just pi instead of 2pi because one period of tan is from (-pi/2, pi/2)

If the question asks for the solutions in the interal [0,2pi) then the answers would just be pi/4?

2. Solve the equation in the interval [0,2pi)
2 cos^2x+sinx=1

For all solutions of the above I got 7pi/6 + 2npi; 11pi/6 + 2npi; pi/2 + 2npi
So, for the interval [0,2pi] would it just be pi/2, 7pi/6, 11pi/6
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April 23rd, 2009, 10:42 AM   #2
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Re: Trig Interval Question

Here is some additional work for #1 and #2

1. tanxcosx-cosx=0

cosx=0 thus x is pi/2 and 3pi/2 but when checked yields error
tanx=1 @pi/4

2. 2cos^2x+sinx=1
sin x=-1/2 @7pi/6 and 11pi/6
sin x =1 @pi/2
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