Question

Find all solutions to the equation.

(sin x)(cos x) = 0

Answer 1

either sin x = 0 or cos x 0

Answer 2

this is due to the zero property of multiplication

Answer 3

These are the options they gave me:

Answer 4

Would it be the first one?

Answer 5

so, at what points are sin(x) = 0 and cos(x) = 0?

Answer 6

check your Unit Circle, if you don't have one, you'd need one, many online

Answer 7

It would be the second one then right?

Answer 8

Because 0 is at 0, pi/2, pi, and 3pi/2

Answer 9

yes, the notation pretty much is just saying,
every \(\large \frac{\pi}{2}\) increment onwards

Answer 10

and yes, at ever \(\frac{\pi}{2}\) either sine or cosine will zero out

Answer 11

Or would it be the 4th one because that one says every pi/2

Answer 12

those 2 look identical to me :/

Answer 13

The second option is pi/2 + n pi & n pi
The fourth one is just pi/2 + n pi

Answer 14

yes, but the restrictions application seem to be exactly the same for the exact same elements

Answer 15

Which do you think would be a better answer then?

Answer 16

the 2nd one is just more redundant

Answer 17

I think the second one instead of the fourth but I'm not sure

Answer 18

I see nothing wrong with either, but I guess go for the redundant one heheh