what is the meaning of () in sin(2x) vs sin2x?

Question

and if you can explain the meaning behind this ?


thanks!!

Answer 1

The parenthesis just clarifies what the angle you want to be when you find the sine value.



like sin(2x) means you evaluate the sine value at angle (2x),



Whereas sin2x means well, you could mean sin(2x), but if you take it bit by bit, that would ultimately mean you take the value of sine at 2 ---> sin(2) times x ------> sin(2) * x...whatever x maybe...



So...there's a difference when you actually look at values:

let x = π/2



sin(2x)

= sin(2(π/2))

= sin(π)

= 0



Whereas...

sin2x

= sin(2) * x



Plug sin(2) in calculator (make sure it's in radian mode)

= 0.9093 * π/2

= 0.45465π



So, we can see that 0.45465π and 0 are two totally different values. So depending on the parethesis, the problem solver can interperet in two different ways: So....basically...make sure to always put parentehsis where it may cause some confusion.



Hope this helps :D

Answer 2

sin(2x) means to DOUBLE x, and then take the sin of the result. Thus if x = 30, then sin(2x) = sin (2*30) = sin 60 = .866



sin2x means (sin x)^2 which is really sinx squared. It prob shows up really crappy in text (unless youre able to raise the 2 and make it smaller), sooo, if x=30, then sin2x = (sin 30)^2 = (sin 30)*(sin 30) = .5*.5 = .25



Hope this helps and does not overexplain. I wanted to be thorough.





Be careful with other answers (Stephen and Crafty are both wrong. Sorry guys)

EDIT: didnt totally read question right-- Whenever you see parentheses, you evaluate the inside of the parentheses FIRST, and THEN you complete the rest. So in sin(2x) you double the x first and then you take the sin. Think of whatever is inside the () as "do me first".

so (2 x 2) + 2 = 4+2 =6, BUT.. 2 x (2 + 2) = 2x4= 8

Now sin2x (which has no parentheses might LOOK like sin2 and then multiple by x, BUT in trig, a number after the sin operation is usually implied to be an exponent. It can be confusing which is why its SOOOO important to use parentheses in trig. sin2x really means (sinx)^2. If they meant sin2 times x then they should use parentheses and say (sin2)x

Answer 3

The parentheses () are used for grouping.



sin (2x) = sin 2x because the usual order of operations is to do multiplication before trig functions. But if you had sin x + 2 that would be ambiguous. Parentheses can be used to distinguish sin(x) + 2 from sin(x+2).

Answer 4

the brackets just make it obivous what you are taking the sin of, other possible meanings that it could look like if the brackets were not there are:



sin^2 x, which means (sin x)^2

(sin 2)*x

there's a few others



so the brackets are just there to make it clear, nothing else.

Answer 5

Parenthesis are used in Mat to encase the figures that are affected by another expression. Sometimes they are not necessary when there is no possibility of a mistake as in the case of your question.

Answer 6

It's just notation.



sin2x might mean xsin2



Putting brackets around both indicate that both are inputs to the sine function.