Question

Find all solutions in the interval [0, 2π).

2sin^2 x = sin x

Answer 1

The temperature of a liquid decreases steadily over several hours. If you calculate the total change in temperature after several hours, will your answer be positive or negative? Explain using the sign rules of multiplication or division

Answer 2

\[2\sin^2(x) - \sin(x) = 0\]Take \(\sin(x) = y\).\[2y^2 - y = 0 \Rightarrow y(2y - 1) = 0 \Rightarrow y = 0~\rm or ~ \dfrac{1}{2} \Rightarrow \sin(x) = 0 ~ or ~ \dfrac{1}{2}\]

Answer 3

List the solutions of \(\sin(x) = 0\) and \(\sin(x) = \dfrac{1}{2}\)

Answer 4

2sin^2x-sinx=0
sinx(2sinx-1)=0
either sinx=0 or 2sinx-1=0
x=0,pi,3pi, and sinx=1/2
x=npi and sinx=pi/6,5pi/6