Question

how do I solve for x?
\[sin(9x)=0\]

Answer 1

no

Answer 2

can you solve \(\sin(y)=0\)

Answer 3

can't you just do this
\[y=cos^{-1}(0)\]

Answer 4

or I can use a unit circle cant I?

Answer 5

what values of y is the sine of y zero.

I'll give a couple

sin(0)=0
\[
\sin(\pi)=0\]

Answer 6

ok I understand that... I'm getting throw off by the 9

Answer 7

so ... can you give me all the solutions to \[\sin(y)=0\]

Answer 8

then we will take care of the 9

Answer 9

ok I can do that \[y=\frac{\pi}{2},\pi,0, and \frac{3\pi}{2} \]

Answer 10

pi/2 and 3pi/2 are not solutions

Answer 11

shoot you are right that is for cos

Answer 12

but 2pi is
3pi, 4pi
-pi
-2pi

Answer 13

to be fair I'm gonna need that for this problem in a bit =)

Answer 14

\[-\frac{\pi}{27}< x < \frac{\pi}{27}\]

Answer 15

so solve \(\sin(9x)=0\) when \(-\dfrac{\pi}{27}< x < \dfrac{\pi}{27}\)

Answer 16

?

Answer 17

yes

Answer 18

then there is only one solution

Answer 19

when sin(0)=0

x=0

Answer 20

the next largest solution would be \(sin(\pi)=0\)

and so \(9x=\pi\) ans \(x=\dfrac{\pi}{9}\) which is outside the interval (same for -\(\pi\))

Answer 21

so x=0

Answer 22

yes

Answer 23

so for cos(9x)=1/2
would I use pi/3?

Answer 24

no that too big right?

Answer 25

on what interval? same?

Answer 26

yes

Answer 27

well \(\cos(\pi/3)=1/2\)

set \[9x=\pi/3\]

so \[x=\pi/27\]

is a solution

but it is not in your interval

Answer 28

same goes for \(-\pi/3\)

so there are no solutions on \(-\dfrac{\pi}{27}< x < \dfrac{\pi}{27}\)

Answer 29

Thank you so much

Answer 30

if it were on the interval \(-\dfrac{\pi}{27}\le x \le\dfrac{\pi}{27}\)

then \(-\pi/27\) and \(\pi/27\) would be solutions

Answer 31

actually, isnt there two solutions for sin(9x)=0 ?

Answer 32

what would the other solution be?

Answer 33

when x=20

Answer 34

because sin(0)=0 and also sin(180)=0

Answer 35

this is in radians

Answer 36

180\(^\circ\) is the same as \(\pi\)rad and \(\pi\) is not a solution

Answer 37

since it is on within our interval \(-\dfrac{\pi}{27}< x < \dfrac{\pi}{27}\)

Answer 38

in particular \(\pm\dfrac{\pi}{9}\) is ont in the interval

Answer 39

oh ok. nvm. i did not know there was a restriction