Question

List the discontinuities for the function f(x) = cot(5x/3 ).

Answer 1

\[\cot\frac{ 5x }{ 3 }\]

Answer 2

what is the value when x = 0?

Answer 3

THESE are the answeres:

a. There are no discontinuities.
b. n(pi/2), where n is an integer
c. n(pi/3), where n is an integer
d. n(three(pi)/5), where n is an integer

Answer 4

how?

Answer 5

@l_o_w_key @cwrw238

Answer 6

cot(x)=cos(x)/sin(x)...
you need to basically solve
\[\sin(\frac{5x}{3})=0\]

Answer 7

what happened to cos?

Answer 8

@myininaya

Answer 9

you can't divide by 0

Answer 10

you have sin(5x/3) on bottom

Answer 11

you cannot have sin(5x/3)=0

Answer 12

i still dont get it

Answer 13

@myininaya

Answer 14

\[\cot(\frac{5x}{3})=\frac{\cos(\frac{5x}{3})}{\sin(\frac{5x}{3})}\]
agreed?

Answer 15

ya

Answer 16

no

Answer 17

a fraction is discontinuous when its bottom is 0

Answer 18

\[\sin(\frac{5x}{3})=0 \text{ will give discontinuites }\]

Answer 19

oh, sorry

Answer 20

it's cotangent, I thought it was cosine

Answer 21

I should pay more attention to the questions.

Answer 22

okay so how do i solve the problem to get the answer?

Answer 23

let u=5x/3
do you know how to solve sin(u)=0

Answer 24

when you are done solve sin(u)=0 for u
then you can finish up by replacing u with 5x/3
then solve for x

Answer 25

i dont know how to do tht

Answer 26

how do u do tht

Answer 27

go to your unit circle and find for what angles is sine (the y-coordinate ) 0

Answer 28

squareroot 3/2

Answer 29

that's an angle?

Answer 30

I think you just randomly chose a value within one of the ordered pairs

Answer 31

I'm asking you to find angle(s) on the unit circle for which the y-coordinate is 0 (0 means zero)

Answer 32

120 and 300

Answer 33

sin(120) is not zero
sin(300) is also not zero

Answer 34

ohh okay so its 180 and 360
.

Answer 35

???

Answer 36

yes and you can also so 0 right?

Answer 37

0,180,360,...
or 180*n
where n is an integer

Answer 38

I think they want it in radians so convert that to radians

Answer 39

\[\frac{5x}{3}=\pi n\]

Answer 40

finish solving for x and you are done

Answer 41

so its pi/2?

Answer 42

trying to think how you got that after solving for x

Answer 43

to undo the division by 3 multiply by 3 on both sides
to undo the multiplication by 5 you divide both sides by 5