# Maths question - multiplying by sin

1. Oct 28, 2008

### questions_uk

hi there. I have an expression Sqrt of 0.6 / 0.2 x sin ^2 however it is giving an error on the calculator.

the equation am trying to work out is :

x = 25 x 10 ^ - 9 x sin ^ - 1 (Square Root of 0.6 / 0.2 x sin ^ 2) (4 x 25)) / ∏ x 4 x 10 ^ - 6

how can I work out x when am getting errors from putting? are the numbers 0.6 and 0.2 no valid for the sin domain? thanks

2. Oct 28, 2008

### phyzmatix

I just want to see this in a "normal" equation form first (find this extended formula notation rather confusing), is your equation:

$$x=25\times10^{-9} \sin^{-1}(\frac{\sqrt{\frac{0.6}{0.2}}\sin^2[(4)(25)]}{4\times10^{-6}\pi})}$$

?

3. Oct 28, 2008

### HallsofIvy

Yes, that will give an error! sin^2 is meaningless. sine of WHAT number? In fact, I notice that you titled this "multiplying by sin". I assumed at first that was just a short way of writing "multiplying by sin(x)" but now I am wondering. Surely you understand that "sin" is a function, not a number- and you multiply both sides of an equation by number; sin(x) is a number.

Last edited by a moderator: Oct 28, 2008
4. Oct 28, 2008

### questions_uk

Yes.

5. Oct 28, 2008

### questions_uk

Hi. thanks for the reply. It is supposed to multiplied by a number ( ^-9) or (and which I think is the case) by the numbers in the bracket.

6. Oct 28, 2008

### HallsofIvy

Well, "^-9" is not a number! And, in any case, sin(x) does NOT mean "sin multiplied by x".

7. Oct 28, 2008

### questions_uk

Yeah I figured the latter bit. Say 25 x 10 ^ - 9 x Arcsin (Square Root of 0.6 / 0.2 x sin ^ 2) (4 x 25)) / ∏ x 4 x 10 ^ - 6)

Would the first thing not be to work out everything in the bracket then multiply it by arcsin? So take Square Root of 0.6 / 0.2 x sin ^ 2 bit first. Sqrt of 3 = 1.7 then x sin ^ 2. How would this be done?

8. Oct 28, 2008

### phyzmatix

You can't multiply by arcsin. Arcsin isn't a number, it's a function. I think you need to touch up a bit on your knowledge of trigonometry here.

Last edited: Oct 28, 2008
9. Oct 28, 2008

### phyzmatix

10. Oct 28, 2008

### questions_uk

Listen, the equation I have is the one that was mentioned, and there is an Arcsin next to 25 x 10 ^ -9 as well as the bracket. am trying to solve for x here. I havent done this kind of maths in a good while.

11. Oct 28, 2008

### phyzmatix

What HallsOfIvy and myself are trying to say is that you CAN'T multiply by sin or arcsin...They are functions. You CAN, however, multiply by sin(x) and arcsin(x). In other words (x)sin is meaningless, but sin(x) isn't.

If you don't understand this, then there is no way you will solve your problem (if indeed a solution exists).

12. Oct 29, 2008

### questions_uk

I'm not, but I worked it out and got a value anyway (not sure if it is right though!). Either way, thank you for your reply. it's appreciated. I did assumed sin ^ 2 (4 x theta) was sin ^ 2 multiplied by (4 x theta).

13. Oct 29, 2008

### Staff: Mentor

It's not "multiplied by."

You might be using a calculator to correctly compute sin^2(4* theta), but you're still not understanding what Halls and phyzmatix have been saying -- that sin, arcsin (AKA sin^(-1), and sin^2 are not numbers that you can multiply other numbers by.

The buttons labeled sin, cos, tan, log, ln, e^x, and others are functions. Each of them performs a specific operation to whatever is showing on the display of the calculator.

14. Oct 29, 2008

### HallsofIvy

It might just be a translation problem.

15. Oct 29, 2008

### phyzmatix

So does that mean everything is ok now? I hope so

Good point.

16. Nov 1, 2008

### questions_uk

Yes I know and thanks. I assumed firstly that it was the function multiplied by a constant. but anyway, got a couple of values that seem on par with vales in the lecture notes so that's good! cheers.