Question

Math help !

Answer 1

@terenzreignz

Answer 2

Domain of validity would simply be the domain of the csc function

Answer 3

Alrighty, What's next?

Answer 4

That's it. Just find the domain of the csc function, and that'd be your answer.

Answer 5

There a set of real numbers right ?

Answer 6

All of it? No. There are certain real numbers that are not in the domain of csc.

Answer 7

Is it a set of real number except for multiples of pi

Answer 8

That's much better :)

Answer 9

Because multiples of pi make sin(x) equal to zero, meaning 1/sin(x) would be 1/0, which can't be allowed.

Answer 10

So this phrase "Is it a set of real number except for multiples of pi" would be my answer ?

Answer 11

Of course not, that's a question. Be more confident...
<ehem>
"The set of real numbers except for multiples of pi"

LOL
or, in notation, it would be
\[\LARGE \mathbb{R} \backslash \left\{n\pi \left| \quad n \in \mathbb{Z}\right.\right\}\]

Answer 12

Simplify trigonometric expression

Answer 13

Okay, I need you to recall that...
\[\LARGE x^2-y^2 = (x+y)(x-y)\]

remember? :)

Answer 14

Yes, remember.

Answer 15

Okay, great... now, can you express \(\large \sin^2 \theta\) in terms of cos?

Answer 16

Correct. One bad news. My calulator died & i don't have batteries for it lol

Answer 17

There is no need for calculators (hopefully) and you have google.
Anyway, if you do know, then express \(\large \sin^2 \theta \) in terms of cos.

Answer 18

yes correct.

Answer 19

Correct?? I just asked you a question :/

Answer 20

Sorry i didn't write that. what do you mean by the express sin^2 theta of cos ?

Answer 21

I mean just that... express sin^2 in terms of cos... Recall the pythagorean identity
\[\Large \sin^2 \theta + \cos^2 \theta = 1\]
And just solve for \(\large \sin^2 \theta\)

Answer 22

Oh okay so would my answer be 1+sin (theta) over cos(theta) ?

Answer 23

Don't jump to conclusions, we will do this step-by-step.
So... solving for \(\large \sin^2 \theta\) from the pythagorean identity, what do you get?

Answer 24

I'm a little confused how could i solve that

Answer 25

It's simple... using algebraic manipulation, just bring everything that is not \(\large \sin^2\theta\) to the other side.

Answer 26

I just have to work on this problem because i don't really understand .

Answer 27

All I really needed you to do was
\[\Large \sin^2 \theta + \cos^2 \theta = 1\]

subtract \(\large \cos^2 \theta\) from both sides...
\[\Large \sin^2 \theta + \cos^2 \theta \color{red}{-\cos^2 \theta} = 1\color{red}{-\cos^2 \theta}\]

Answer 28

Simplifying, we get...
\[\Large \sin^2\theta = 1- \cos^2 \theta\]

Answer 29

And that's how to express \(\large \sin^2 \theta\) in terms of cos.

Answer 30

Ohhhhhhhhh okay now i see. So after we do that what do we do to get the answer ?

Answer 31

Take a good look at the right-side of the equation... does it look familiar to you?
\[\Large \sin^2\theta = \color{blue}{1- \cos^2 \theta}\]
I asked you to recall that
\[\large x^2 - y^2 = (x+y)(x-y)\]

Something similar can be done to the right-side of the equation...

Answer 32

with that 1-cos^2(theta) will it be over sin(theta)

Answer 33

Don't get ahead of yourself... using what I asked you to recall
(namely that \(x^2 - y^2 = (x+y)(x-y)\) )

Factor the right side... of this equation
\[\Large \sin^2\theta = \color{blue}{1- \cos^2 \theta}\]

Answer 34

I'm still not understanding

Answer 35

maybe a simple tweak?
\[\large 1 = 1^2\]
\[\Large \sin^2 \theta = 1-\cos^2 \theta = \color{blue}{1^2 -\cos^2 \theta}\]

Answer 36

ok

Answer 37

This pattern... use it...\[\huge x^\color{red}{2}-y^\color{red}2= (x+y)(x-y)\]

Answer 38

okay i understand that by looking at it

Answer 39

Well, you have to learn to recognise it.. it's here...
\[\Large \sin^2 \theta= \color{blue}{1^2 - \cos^2 \theta}\]

Answer 40

The pattern is called the difference of two squares.

Answer 41

Okay got that

Answer 42

So...?

Answer 43

Do i solve that above

Answer 44

To be blunt...
\[\large x^2 - y^2 \] factors into
\[\large (x+y)(x-y)\]

so to what does
\[\Large 1^2 - \cos^2 \theta\]factor into?

Answer 45

1^2 + cos^2(theta)

Answer 46

I suggest you review factoring "difference of two squares"...

Answer 47

I am going to review after we finish this problem. I know your trying to go to bed now

Answer 48

Yes... yes you do :)
but how can we finish this problem without knowing how to factor a difference of two squares? :)

Answer 49

I can just re view after this problem lol

Answer 50

Very well.. then back to my query...
to what does
\[\Large 1^2 - \cos^2 \theta\] factor into?

Answer 51

I thought i just answered this 3 times lol

Answer 52

Three times incorrectly. Reread through what I asked you to recall before we even started working on this problem, the answer is there...

Answer 53

Now, was that really necessary? :D

Answer 54

Haha no i just want you to go to sleep

Answer 55

Oh, trust me, I do want to go to sleep... :)
but I don't like leaving things undone...

I'll finish this or die trying... so to speak...

Now, my request? That factoring thing?

Answer 56

Are we back to the factoring thing. I just need to finish this one i have 20 more problems to go.

Answer 57

Well, then, let's finish it :)

Starting with factoring that expression there...

Answer 58

Okay is there an easy way to do this because im conused. You can just go to bed ill just skip this problem

Answer 59

Is that giving up?

Answer 60

Well no lol i just dn't understand

Answer 61

Well, while you're at it, review factoring a difference of two squares... it comes in handy in trig.

Answer 62

i am going to review .

Answer 63

Good. That's all I want to know :)
-------------------------------------
Terence out

Answer 64

Whats the answer ?