If sine θ is a function, why does it not have parentheses?

[yj1214]

This is not really a mathematical question but rather a question of math "Grammar" if that is what it's called.


Anyway trig functions are usually written as,

sine θ = Opp / Hyp

cos θ = Adj / Hyp

tan [FONT=Georgia, Times, Times New Roman, serif]θ = Opp / Adj[/FONT]


[FONT=Georgia, Times, Times New Roman, serif]and functions are written as,[/FONT]

[FONT=Georgia, Times, Times New Roman, serif]f(x) = something...
[/FONT]

[FONT=Georgia, Times, Times New Roman, serif]and I was just wondering why trig functions don't have parentheses around their name?

like this,

[/FONT]
sine(θ) = Opp / Hyp

cos(θ) = Adj / Hyp

tan([FONT=Georgia, Times, Times New Roman, serif]θ) = Opp / Adj


is there a reason why people don't put parentheses around the name of trig functions?

or is it just a preference?
[/FONT]

 

[Deleted member 4993]

This is not really a mathematical question but rather a question of math "Grammar" if that is what it's called.


Anyway trig functions are usually written as,

sine θ = Opp / Hyp

cos θ = Adj / Hyp

tan θ = Opp / Adj


and functions are written as,

f(x) = something...


and I was just wondering why trig functions don't have parentheses around their name?

like this,


sine(θ) = Opp / Hyp

cos(θ) = Adj / Hyp

tan(θ) = Opp / Adj


is there a reason why people don't put parentheses around the name of trig functions?

or is it just a preference?

The only reason I can think of is laziness. I was taught to use sin(Θ) and I use it thus!!

 

[ksdhart2]

The only reason I can think of is laziness. I was taught to use sin(Θ) and I use it thus!!

I concur with this. That's how I was taught as well. Sometimes, I'll see people write something like sin 3x. While it's generally clear what they meant, the literal interpretation of that is: sin(3) * x. Actually, I once completed a homework problem with two versions... "Assuming sin 3x means sin(3) * x: ..." and "Assuming sin 3x means sin(3x): ..." Needless to say, my teacher was not amused. >.>

 

[pka]

The only reason I can think of is laziness. I was taught to use sin(Θ) and I use it thus!!

I too agree with the above, particularly the remark on laziness. However, I will argue that the non-use of parenthesis is a hangover from history. Mathematics history is replete with examples of hundreds of years in with lack of formulation served well. Current function notation is really quite new in the context of history. In Newton's era those active in mathematics and seeing \(\displaystyle \sin 30\) would recognize applying the sine concept to 30. Likewise, they would have concurred upon seeing \(\displaystyle \sin^2~\theta\) as opposed to \(\displaystyle \sin~\theta^2\).

But I think with the explosion of notation we should adopt a standard notation for functions.

 

[stapel]

I agree with the "laziness" answer, too. I would add that this laziness often leads to student confusion, in thinking somehow that the parentheses, when they are used, somehow mean "multiplication" (which of course they don't), and pushes students to dropping the arguments altogether, leaving them utterly confused halfway through many homework (and test) questions.

The original poster is correct: one should always use the parentheses for trig functions!

 

[Otis]

... one should always use the parentheses for trig functions!

For sure! I advocate for proper function notation with all functions. Why be lazy?

Plus, we increasingly will need to interact with machines. Software usually requires proper function notation.

 

[Steven G]

This is not really a mathematical question but rather a question of math "Grammar" if that is what it's called.


Anyway trig functions are usually written as,

sine θ = Opp / Hyp

cos θ = Adj / Hyp

tan θ = Opp / Adj


and functions are written as,

f(x) = something...


and I was just wondering why trig functions don't have parentheses around their name?

like this,


sine(θ) = Opp / Hyp

cos(θ) = Adj / Hyp

tan(θ) = Opp / Adj


is there a reason why people don't put parentheses around the name of trig functions?

or is it just a preference?

I'm lazy and I DO use parenthesis.