Why sinx.sinx = sin²x not sin²x²?

[Indranil]

Why sinx.sinx = sin²x not sin²x²?

As we know x.x = x²,so sin.sin = sin² but, Why sinx.sinx = sin²x not sin²x²? Please explain.

 

[mmm4444bot]

… sin.sin = sin² …

This is not correct.

'sin' is not a number, so you may not square it.

'sin' is a name. It refers to the Sine function.

Have you learned about function notation? If not, now is the time to google it and learn (i.e., before you study trigonometry).

Sine is one of the six trigonometric functions. We input an angle measurement (call it x) into the sine function, and the function outputs the angle's sine value.

sin(x) is function notation for the output.


Therefore, the notation sin²(x) means the square of the number sin(x).

sin²(x) = sin(x) ⋅ sin(x)

For example, the sine of 30° is 1/2. In other words, if we input 30° into the sine function, the output is 1/2.

sin(30°) = 1/2

sin²(30°) = (1/2)(1/2) = 1/4 :cool:

 

[Steven G]

As we know x.x = x²,so sin.sin = sin² but, Why sinx.sinx = sin²x not sin²x²? Please explain.

sin has no meaning at all, so sin*sin has no meaning.

Think of f(x) and just writing f. It has no meaning. You can find/calculate f(x), f(2), f(7.897); but not f. Similarly you can calculate sin(x) or sin(2pi/3), but you can't compute sin.

It seems that you think that sin x = sin*x which is NOT true. sin(x)*sin(x) = (sin(x))² and we have an alternate way of writing that which is sin²(x).

I am very glad that you asked this question as you really need to understand why what you said was wrong. If you have any questions about this please reply to the post.

 

[Dr.Peterson]

As we know x.x = x²,so sin.sin = sin² but, Why sinx.sinx = sin²x not sin²x²? Please explain.

It's important to understand that sin²x is a special notation that is inconsistent with other notations, and is defined to mean (sin x)², that is, the square of the result of the sine function -- which is exactly what sinx.sinx means. It goes back to a time when parentheses were not used for the argument of functions, as they typically are today, and if they wrote sin x², it would have been read as sin(x²), and is entirely different.

In fact, for other functions, the notation f²(x) would usually mean that the function is applied twice (composition): f(f(x)). The notation f^-1(x) goes with this concept.

You may find these discussions interesting: here and here.