Question

my teacher said
'if sec(x)=sec(y), then x=y' is a false statement
why is this?

Answer 1

because sec is a periodic function. so it can take on many values of x and y which results in the same sec value.

Answer 2

..... yep, one value can have many names

Answer 3

so we can say x=y+2npi
for n is an integer
right?
would that make the statement true?

Answer 4

The secant function is not injective so there is no unique inverse function. ;)

Answer 5

sec(x) = sec(y) is the same as cos(x) = cos(y) and cos is has a period of 2pi. so yes.

Answer 6

if we put john on a merry-go-round and turn him pi/2 ; and take billy and turn him 5pi/2

the sec(john) = sec(billy) ; even tho john does not equal billy

Answer 7

lol

Answer 8

cot(x)*tan(x)=1 is false since
cot(x)=cos(x)/sin(x) and sin(x) is sometimes 0
just like
tan(x)=sin(x)/cos(x) and cos(x) is sometimes 0

Answer 9

seriously monkey131? I don't quite agree with you on that hmm.

Answer 10

the problem is that when sin(x) is 0 and blahblah there will always be a denominator with a 0. those values are undefined for the tangent/cotangent function.

Answer 11

well we can't have divsion by 0
so it would be true if they said whenever cot(x) and tan(x) is not 0

Answer 12

when sin(x) = 0 the value of tan(x) is not defined. so it wouldn't be considered as a falsified statement.

Answer 13

i mean cos(x).

Answer 14

both when both are 0 the equality fails

Answer 15

you can't have both being 0 at the same time.

Answer 16

right and you can't have 0=sin(x) and 0=cos(x)
but also if sin(x)=0 or cos(x)=0 the equality fails
but i guess and wouldn't happen
sin(x) is not zero the sametime cos(x) is 0

Answer 17

so they would never be zero at the same time

so if just one of them is zero then the equality fails

Answer 18

yup that's true. but you're assuming that 0 * infinity is not 1. what is 1/0 * 0 for all you know it could be 1!

Answer 19

ok you lost me there

Answer 20

ok you lost me there

Answer 21

if tan(x) = 0 cot(x) = 1/0

Answer 22

right i was say we can't have cos(x)=0 and we can't have sin(x)=0

Answer 23

we cannot have either case

Answer 24

yeah that was what i said earlier. If that is not possible then the case where it is 0 is not possible and the statement isn't false.

Answer 25

i mean statement isn't true.

Answer 26

yeah that is what i was saying in the beginning

Answer 27

O.o but you claimed that cot(x)*tan(x) is false

Answer 28

cot(x)*tan(x) = 1 is false*

Answer 29

yes it is false

Answer 30

it is true when sin(x) does not equal 0 or when cos(x) does not equal 0

Answer 31

but we cannot suppose that what is not given

Answer 32

they cannot equal 0 since for those values where they are either tan(x)or cot(x) does not have a definite value.

Answer 33

so the statement is false

Answer 34

yep

Answer 35

it is true as far as all mathematical definitions is concerned.

Answer 36

that cot(x)tan(x)=1?

Answer 37

probably. define tan(90 degrees)

Answer 38

cot(x)tan(x) does not always equal 1 as we pointed out above
sometimes it is undefined for certain values like x=0 or x=pi/2

remember cot(x)=cos(x)/sin(x)
so cot(pi/2) is undefined

Answer 39

oops tan(pi/2) is undefind

Answer 40

what is (1/0)*0 why can't it be 1?

Answer 41

because its not 1

Answer 42

thats an underiminate form
a form that cannot be determined

Answer 43

thats an underiminate form
a form that cannot be determined