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# Why is sin x a function?

Updated: 12/23/2022

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Q: Why is sin x a function?
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### The function y equals sin θ is not a function beacause sin 30 equals sin 150?

Y=sin X is a function because for each value of X, there is exactly one Y value.

y= sin 3x

### How is the function x plus sin x best described?

It is an increasing odd function.

### What is the significance of the x-value in a sine wave function?

The answer will depend on where, in the sine function, the x-value appears: For example, its roles in f(x) = sin(x), or f(x, theta) = x*sin(theta) or f(x, theta) = sin(x*theta) f(theta) = sin(theta + x) are quite different.

### Is Sin x a constant?

No, it's a function.

### What is the period for y-3 sin x?

y = 3 sin x The period of this function is 2 pi.

### 2 sin x - 3 equals 0?

2 sin(x) - 3 = 0 2 sin(x) = 3 sin(x) = 1.5 No solution. The maximum value of the sine function is 1.0 .

### What is sine squared?

Answer 1 Put simply, sine squared is sinX x sinX. However, sine is a function, so the real question must be 'what is sinx squared' or 'what is sin squared x': 'Sin(x) squared' would be sin(x^2), i.e. the 'x' is squared before performing the function sin. 'Sin squared x' would be sin^2(x) i.e. sin squared times sin squared: sin(x) x sin(x). This can also be written as (sinx)^2 but means exactly the same. Answer 2 Sine squared is sin^2(x). If the power was placed like this sin(x)^2, then the X is what is being squared. If it's sin^2(x) it's telling you they want sin(x) times sin(x).

### What does the S in sin mean?

Whenever you see a function such as the sine function, you have to see the function as a whole. The "s" doesn't mean anything by itself in this case; sin(x) means the sine of an angle x.

### Express as a single sine or cosine function 6 sin x cos x?

sin(2x)=(1/2)sin(x)cos(x), so 6sin(x)cos(x)=12sin(2x)

Neither.

### How you can defferentiate an integral?

If the upper limit is a function of x and the lower limit is a constant, you can differentiate an integral using the Fudamental Theorem of Calculus. For example you can integrate Integral of [1,x^2] sin(t) dt as: sin(x^2) d/dx (x^2) = sin(x^2) (2x) = 2x sin(x^2) The lower limit of integration is 1 ( a constant). The upper limit of integration is a function of x, here x^2. The function being integrated is sin(t)