Question

Find all solutions in the interval [0, 2π).
(sin x)(cos x) = 0

A. pi/2, pi
B. 0, pi/2, pi, 3pi/2
C. pi, 3pi/2
D. 0, 3pi/2

Answer 1

`cos(x) = 0` when?
`sin(x) = 0` when?

Answer 2

cos(0) is not zero, but sin(0) is zero.
So your first solution is x=0.

can you tell me some more solutions?

Answer 3

Given the options, 3pi/2 is a solution. However I'm not exactly sure how.. I'm lost on this one.

Answer 4

\(\large\color{black}{ 3\pi/2 }\) is the same as \(\large\color{black}{ 270 }\) degrees.
and what is zero, sin(270) or cos(270) ?

Answer 5

sin(270)= -1
cos(270)= 0

Answer 6

so cos(270)

Answer 7

yes

Answer 8

This is why \(\large\color{black}{ 3\pi/2 }\) is one of the solutions.

Answer 9

okay, and knowing (from what we said before) that zero is one of the solutions, you now have \(\large\color{black}{ B }\) or \(\large\color{black}{ D }\), right?

Answer 10

Then, try \(\large\color{black}{ \pi/2 }\) and \(\large\color{black}{ \pi ~. }\)

Answer 11

1) the sine or the cosine of \(\large\color{black}{ \pi/2 }\) is zero?
2) the sine or the cosine of \(\large\color{black}{ \pi }\) is zero?

Answer 12

sin(pi/2)= 1
cos(pi/2)= 0 **

sin(pi)= 0 **
cos(pi)= -1

Answer 13

1) cosine
2) sine

Answer 14

yes.

Answer 15

And which option will you pick as your final answer?

Answer 16

B?

Answer 17

Yup:)

Answer 18

Thank you so much! :)

Answer 19

No problem.