My Math Forum Trig Interval Question

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 April 23rd, 2009, 10:30 AM #1 Newbie   Joined: Apr 2009 Posts: 3 Thanks: 0 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) tanxcosx-cosx=0 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
 April 23rd, 2009, 10:42 AM #2 Newbie   Joined: Apr 2009 Posts: 3 Thanks: 0 Re: Trig Interval Question Here is some additional work for #1 and #2 1. tanxcosx-cosx=0 cosx(tanx-1)=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 2(1-sin^2x)+sinx-1=0 2-2sin^2x+sinx-1=0 -2sin^2x+sinx+1=0 -1(2sinx+1)(sinx-1)=0 2sinx+1=0 sin x=-1/2 @7pi/6 and 11pi/6 sinx-1=0 sin x =1 @pi/2

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# 1/sinx cosx interal

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