# Sin Cube x Formula, Proof | Sin^3x Formula

The sin cube x formula is given as follows: sin3x = (3sinx -sin3x)/4, that is, sin^3x formula is equal to (3sinx – sin3x) divided by 4. Here we establish the formula of sine cube x and give a proof.

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## What is sin cube x formula

Answer: sin3x = (3sinx -sin3x)/4

Proof:

To establish the formula of sin^3x, we will use sin3x formula which is provided below:

sin3x = 3sinx – 4sin3x.

Adding -3sinx to both sides, we get that

– 3sinx + sin3x = – 3sinx + 3sinx – 4sin3x

⇒ – 3sinx + sin3x = – 4sin3x

⇒ 3sinx – sin3x = 4sin3x (changing the signs)

Dividing both sides, we obtain that

(3sinx – sin3x)/4 = sin3x.

So the sin3x formula is given by sin3x = (3sinx – sin3x)/4 and this is proved by using the formula of sin3x.

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## Integration of sin^3x Formula

Using the above sin3x formula sin3x = (3sinx -sin3x)/4, the integration of sin^3x will be calculated as follows.

So the integration of sin cube x is equal to ∫sin3x dx = – (3cosx)/4 + (cos3x)/12 + C where C is an integral constant.

## Derivative of sin^3x Formula

The derivative of sin^3x is calculated as given below.

$\dfrac{d}{dx}(\sin^3 x)$ = $3\sin^2 x \cdot \dfrac{d}{dx}(\sin x)$ = $-3\sin^2 x \cos x$.

So the derivative of sine cube x with respect to x is equal to -3sin2x cosx, that is, d/dx(sin3x) = -3sin2x cosx.

## FAQs

Q1: What is the sin^3x formula?

Answer: sin3x = (3sinx – sin3x)/4 is the formula of sin^3x.

Q2: What is the sin^3θ formula?

Answer: The sin cube theta formula says that sin3θ = (3sinθ -sin3θ)/4.

Q3: What is the formula of sin 3theta?

Answer: Sin 3theta formula is equal to 3 sin theta – 4 sin 3theta.

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