# Why sinx.sinx = sin²x not sin²x²?

#### Indranil

##### Junior Member
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

##### Super Moderator
Staff member
… 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:

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#### Jomo

##### Elite Member
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).