Question

Find all solutions to the equation.

(sin x)(cos x) = 0

a.{npi|n=0,1,2,...}
b.{(pi/2)+npi,npi|n=0,1,2,...}
c.{(pi/2)+2npi|n=0,1,2,...}
d.{(pi/2)+npi|n=0,1,2,...}

Answer 1

can anyone please help? ;(

Answer 2

\(\sin(x)=0\) means \(x=0,\pi,2\pi,...\)

Answer 3

\(\cos(x)=0\) means \(x=\frac{\pi}{2},\frac{3\pi}{2},\frac{5\pi}{2},...\)

Answer 4

@satellite73 so it will be an a?

Answer 5

taken together, it would be \(n\pi\) and \(\frac{\pi}{2}+\pi\)

Answer 6

no, go with \(b\)

Answer 7

\(\{\frac{\pi}{2}+n\pi, n\pi |n\in \mathbb{Z}\}\)

Answer 8

@satellite73 thankyou!!:):)

Answer 9

or if you like \(n=0,1,2,...\) but that is not really correct because \(n\) could be negative

Answer 10

yw