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anonymous
 5 years ago
sin²θcos²θcosθ=1. Find all solutions in the interval [0,2π).
anonymous
 5 years ago
sin²θcos²θcosθ=1. Find all solutions in the interval [0,2π).

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anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0\[sin^2(x)cos^2(x)cos(x)=1\] first rewrite in term of cosine alone, using the identity \[sin^2(x)+cos^2(x)=1\] \[1cos^2(x)cos^2(x)cos(x)=1\] \[12cos^2(x)cos(x)=1\] \[2cos^2(x)cos(x)=0\] \[2cos^(x)+cos(x)=0\] \[cos(x)(2cos(x)+1)=\] \[cos(x) = 0\] or \[2cos(x)+1=0\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0of course you still have to solve \[cos(x) = 0\] \[x=\frac{\pi}{2}\]or \[x=\frac{3\pi}{2}\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0\[2cos(x)+1=0\] \[cos(x)=\frac{1}{2}\] \[x=\frac{2\pi}{3}\] \[x=\frac{4\pi}{3}\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0you have 4 solutions all together.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0oh, ok...also the π/2 and 3π/2.... thanks

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0it is, when someone shows you!

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0mmm rly u have unfintly solutin here by adding the period of ur functin

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0of course! idea is to write using one trig function, then you get a quadratic equation to solve. there are an infinite number of solutions, that is why the question restricts interval from \[[0,2\pi)\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0thanks 'satellite 73' . hard to know where to start.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0mm sry 'm jst dont care 2 the question

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0it is, when someone shows you!

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0oh, ok...also the π/2 and 3π/2.... thanks

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0yes 4 total. two for the equation \[cos(x)=0\] and two for \[cos(x)=\frac{1}{2}\]
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