Question

Is the function f(x)=1/cosx continuous on the interval [0, pi/7] ?

Yes or no?

***don't understand this :( please explain? Thanks :)

Answer 1

Well, if there was some point where cos(x) = 0, then you would have a problem, and it wouldn't be continuous.

Answer 2

how can I determine whether or not there's a point where cos(x)=0 ?

Answer 3

What are the known roots of cos(x)?

Answer 4

ermm i'm not really sure :(

Answer 5

can't remember... does this have to do with the unit circle? Or is it more of one of the rules of cos ?

Answer 6

Use the unit circle.

Answer 7

Or consider a triangle

Answer 8

A right triangle like this
/ |
/ |
/----|

Answer 9

At what angle does the bottom corner need to be for the bottom leg to be 0 length?

Answer 10

umm 1.5 ?

Answer 11

wait that doesn't look right haha... ermm not really sure :(

Answer 12

1.5? Where did you get that? lol It's going to be in terms of pi

Answer 13

When you have a 90 degree angle, it is no longer a triangle but a straight line. Then cos(x) = 0 at 90 degrees.

Answer 14

yeah i'm not even sure haha...

okay.. so would it be pi/2 ?

Answer 15

Yes.

Answer 16

Also -pi/2 would work as well.

Answer 17

okay :)

what happens from here?

Answer 18

The question is does the interval they gave us ever hit these angles?

Answer 19

no? because it only goes to pi/2 ?

Answer 20

It goes to pi/7

Answer 21

ohh okay then yeah it does hit it right?

Answer 22

So it doesn't ever get to +/- pi/2

Answer 23

oh oops... haha my bad :P

Answer 24

pi/2 = 3.5 pi/7

Answer 25

less than pi/7

Answer 26

This means the function is always continuous on this interval.

Answer 27

ahhh i see... so when it does hit, then that means that it's not continuous? and when it doesn't, then it is continuous?

Answer 28

Yes

Answer 29

ohh okay awesome :)

so in this case, it would be continuous ? :)

Answer 30

yes

Answer 31

okay awesome!!! thank youu :)