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Does anyone else find the syntax of trigonometric functions to be counter-intuitive?

Hi,

Just as the title says: does anyone else find the syntax of trigonometric functions to be completely counter-intuitive? For example:

sin A = 1/2

I find it odd that A is the unknown, yet we're not technically isolating it. Instead, because we don't know the value of A, we should be using sin^1(1/2) to find the value of A. So why is it not written this way?

Other than saving a bit of typing, is there another reason it's written the way it is, or am I missing something else entirely?

Reply 1

TenOfThem

Original post by John.H

Really not sure what you are asking

Sometimes you need to find an angle, sometimes you don't

But, how else would we write it - Sin is a function so Sin(A) = b is the only appropriate syntax

Clearly if you want to find A you would write either

Sin^-1(b) = A

or

arcSin(b) = A

Reply 2

John.H

That's exactly my point. I've gone through several different books and resources online, and they're all writing it as:

sin A = a/c

instead of:

sin^1(a/c) = A

where a and c are already known. That implies we need to find A, yet it's not being expressed that way at all, muddling the intention entirely.

Reply 3

VannR

How about this one?:

sin(x)cos(x) = 1 - (5/2)cos(2x), for 0 <- x <- 2(pi) radians

The notation might not make sense for such a simple example, but when you start solving equations like this the notation makes complete sense.

Reply 4

TenOfThem

Original post by John.H

I still do not know what you mean

It is like you are saying that you cannot have e question such as

3x^2 - 5x - 1 = 0

because x is what you are trying to find

In maths we are often asked to solve f(x) = a number to find x

Reply 5

John.H

Original post by TenOfThem

I still do not know what you mean

It is like you are saying that you cannot have e question such as

3x^2 - 5x - 1 = 0

because x is what you are trying to find

In maths we are often asked to solve f(x) = a number to find x

VannR's got the gist of what I'm getting at. I'm not saying we can't write it either way, but surely if you're aiming to solve for a particular unknown, the simplest form of implying that fact is to write the expression in terms of the unknown. For example, if you have a, b, and c, and want to solve for c, you wouldn't leave it in the form a = c/b, which is basically what sin A = 1/2 is doing.

Reply 6

TenOfThem

Original post by John.H

If you are given that the Sine of an angle is 0.5 then you would start with

Sin(A) = 0.5

And that would lead to

arcSin(0.5) = A

Reply 7

John.H

Original post by arkanm

However, if the question is stated as e.g. "If sin A = 1/2, find A, where A is an acute angle", then I think the notation is perfectly fine.

That certainly makes sense, and I agree with that entirely. However, it literally is expressed as sin A = 1/2, and this is not the first time I've seen this. In fact, the very reason I'm posting this is because I'm seeing this on such a regular basis.

Reply 8

TenOfThem

Original post by John.H

Perhaps you could take an shot of an example so that we can see what the problem is

Reply 9

John.H

I'd actually like to do that, but I'm visually-impaired so I don't own a phone. :frown:

I should also say that I appreciate the replies. :smile:

Reply 10

Sataris

I think I know what you mean, but you seem to be complaining about how maths works as a language. Is this like "I love him" vs "He is loved by me"?

Reply 11

TenOfThem

Original post by John.H

I'd actually like to do that, but I'm visually-impaired so I don't own a phone. :frown:

I should also say that I appreciate the replies. :smile:

Reply 12

tazarooni89

The reason is because, the following two equations do not mean exactly the same thing:

[1] Sin(A) = 1/2
[2] A = Arcsin (1/2)

In the first equation, there are many possible values for A, for example 30 degrees, 150 degrees, 390 degrees, 510 degrees etc. The second equation will give you only one value of A, which will lie somewhere in between -90 degrees and 90 degrees.

It's more traditional to write it in the first manner, because it's more broad and indicates there are multiple values of A that would satisfy the equation. Also, Sin is a function defined on the entire real line, whereas Arcsin is only defined for values between -1 and 1, so it's used more like a method of solving the equation rather than as a function in itself.