Question

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

Answer 1

`\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} (\pi )/(2)\\\\ (3\pi )/(2) \end{cases}\\\\ -------------------------------`


`\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} (7\pi )/(6)\\\\ (11\pi )/(6) \end{cases}`