Question

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

(sin x)(cos x) = 0

Answer 1

Explain how to do it please??

Answer 2

Do you have Multiple choice answers?

Answer 3

pi/2, π

0, pi/2, π, 3pi/2

π, 3pi/2

0, 3pi/2

Answer 4

Alright

Answer 5

So. With this problem, you are already at the final step, and all you have to do is match them up on a unit circle. Can you open one please? (:

Answer 6

what do u mean?

Answer 7

Okay let me start here. \[(\sin(x))(\cos(x))=0 \] from this, to solve for both Sin and Cos you make \[Sin(x)=0\] and the \[Cos(x)=0\]

Answer 8

Do you get that?

Answer 9

yeah

Answer 10

Alright and after that you pull out your handy dandy Unit circle

Answer 11

Yep i have one

Answer 12

You know on the unit circle there is (x,y) correct? well on a unit circle the x=cos and the y=sin.

Answer 13

i know that.

Answer 14

So if you look at the equations we just had. \[Sin(x)=0\] and \[Cos(x)=0\] where on the unit circle does Sin=0 and where does Cos=0

Answer 15

sin=0 at0 0,1 and 0,-1

Answer 16

cos=0 at 1,0 and -1,0

Answer 17

oh other way around lol

Answer 18

so sin=0 at 1,0 and -1,0
and cos=0 at 0,1 and 0,-1

Answer 19

Yup :P But what are the Radian measures of that? (i.e \[\frac{ 5\Pi }{ 6 }\]

Answer 20

oh right right....
OHHH those must be the answers right *epiphany* lol
0, pi/2, pi, 3pi/2?

Answer 21

is that right?

Answer 22

Yup :D which is you second answer. Good job ^^

Answer 23

Thanks and thank you for your help :D

Answer 24

No problem. If you ever need anymore help let me know(: