hscwav2012
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5 How many solutions does the equation cos 2θ= sinθ have in the domain 0 ≤ θ ≤ 360?
(A) 2
(B) 3
(C) 4
(D) 5
(A) 2
(B) 3
(C) 4
(D) 5
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Carrotsticks
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(B)
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hscwav2012
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Explain?
Carrotsticks
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Sorry (B), I miscalculated earlier.
 = \sin(x) \\\\ 1-2 \sin^2(x) = sin(x) \\\\ 2\sin^2(x) + \sin(x) -1 = 0 \\\\ (2 \sin(x) -1)(\sin(x) +1) = 0 \\\\ \sin(x) = -1, \frac{1}{2} \\\\ x = \frac{3 \pi}{2}, \frac{\pi}{6}, \frac{5 \pi}{6} )
hscwav2012
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That makes sense, but could this question be done graphically as well:
graphing cos2x & sinx on the same axes in the domain 0<x<360
graphing cos2x & sinx on the same axes in the domain 0<x<360
Carrotsticks
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