Question

Find the domain and range of the following functions:

Answer 1

y=secx

Answer 2

Please explain :/

Answer 3

everywhere except where the \(\cos(x)=0\)

Answer 4

Can i get more explanation :/

Answer 5

y = sec x = 1/ cosx
so all values of x are acceptable except those for which cosx = 0
so now can you sovle for those values of x?

Answer 6

It would be infinity na?

Answer 7

why cannot it be 0 then?

Answer 8

whoops sorry.
range: [1, infinity)

Answer 9

1/0 is not defined
who said it`s infinity

Answer 10

1/0=complex infinity

Answer 11

well let me tell you those are just ways of convincing and infinity as such has no significance
infinity is no fixed point
it`s better if we talk of thing like "it tends to infinity"
so for all those values of x for which function is not defined are excluded from domain

Answer 12

Okay i got the idea so what would be the range?

Answer 13

And domain? @harsimran_hs4

Answer 14

for domain you can take out all odd multiples of pi/2
domain = {all real} - { x = n(pi/2)} where n is an integer
range = {all real} - (-1, 1)

Answer 15

This is not helping :/


Actually i need it right from the basics :/


Please :(

Answer 16

i think domain might be clear?

Answer 17

No :(

Answer 18

tell me general solution of equation
cosx = 0

Answer 19

Ok so

Cosx=0

x=Cos^-1(0)

x=90 degrees or pi/2

Answer 20

well i had asked for general solution not particular
so if i say all odd multiples of pi/2 satisfy this equation
do you agree?

Answer 21

I am not getting the point of odd multiples and what do you mean by general solution :/

Answer 22

x = pi/2 , 3pi/2 , 5pi/2 and so on will also satisfy this equation
agreed?

Answer 23

Sorry,I am not that good :/,How do you know that?

Answer 24

by inspection or
it`s proof is covered in any trignometry book you can refer it

Answer 25

Please explain me i dont have time,Can i ask another which is not related with trigonometry and we can do this later?

Answer 26

i`ll give you some proof intuitively

pi/2 + pi = 3pi/2
so it`s again zero at 3pi/2 and
3pi/2 + pi = 5pi/2 and so on...