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anonymous
 5 years ago
Find all solutions on the interval [0,2pi]
2 cosx sinx  cos x =0
Please show+explain work?
anonymous
 5 years ago
Find all solutions on the interval [0,2pi] 2 cosx sinx  cos x =0 Please show+explain work?

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anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0did you get this yet? if not i will solve.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0first i would write \[2cos(x)sin(x)=cos(x)\] then square to get \[4cos^2(x)sin^2(x)=cos^2(x)\] \[4cos^2(x)[1cos^2(x)]=cos^2(x)\] \[4cos^2(x)4cos^4(x)cos^2(x)=3cos^2(x)4cos^4(x)=0\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0how am i doing so far?

watchmath
 5 years ago
Best ResponseYou've already chosen the best response.2If i do this I will move the cos x to the left and factor out the cos x

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

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

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0proof 2 now that i am on a roll. \[f'(x)=3ax^24ax8a\] the zeros are \[\frac{4a\pm\sqrt{16a^2+96a}}{6a}=\frac{4a\pm4\sqrt{a^2+6a}}{6a}=\] \[\frac{2\pm 2\sqrt{a(a+6)}}{3a}\] and in order for this to be 1 \[a(a+6)\] must be a perfect square, a miracle if ever there

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0ignore that last gibberish it is wrong and not from here anyway.

watchmath
 5 years ago
Best ResponseYou've already chosen the best response.2Alternative solution \(\cos x(2\sin x 1)=0\) \(\cos x=0\Rightarrow x=\pi/2,3\pi/2\) \(\sin x=1/2\Rightarrow x=\pi/6,5\pi/6\).

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0btw we knew \[\pm\frac{\pi}{2}\]worked to begin with by inspection.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0right, much swifter and i retire now. yikes.
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