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What values for theta(0<=theta<=2pi) satisfy the equation?
2 sin theta cos theta+cos theta=0
A) pi/2 , 3pi/4, 3pi/2 , 7pi/4
B) pi/2 , 7pi/6 , 3pi/2, 11pi/6
C) pi/2 ,3pi/ , 5pi/4 , 7pi/4
D) 0, pi/2, pi, 3pi/2

Respuesta :

[tex]\bf 2sin(\theta )cos(\theta )+cos(\theta )=0\implies cos(\theta )[2sin(\theta )+1]=0\\\\ -------------------------------\\\\ cos(\theta )=0\implies \measuredangle \theta =cos^{-1}(0)\implies \measuredangle \theta = \begin{cases} \frac{\pi }{2}\\\\ \frac{3\pi }{2} \end{cases}\\\\ -------------------------------[/tex]

[tex]\bf 2sin(\theta )+1=0\implies 2sin(\theta )=-1\implies sin(\theta )=-\cfrac{1}{2} \\\\\\ \measuredangle \theta =sin^{-1}\left( -\cfrac{1}{2} \right)\implies \measuredangle \theta = \begin{cases} \frac{7\pi }{6}\\\\ \frac{11\pi }{6} \end{cases}[/tex]
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Question:

cos ( 7 pi / 12 ) + cos ( pi / 12 ) =

cos ( 7 pi / 12) - cos ( pi / 12 ) =

Answers:

1. 0.71

2. -1.22

Explanation:

I got it correct in my test :)

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