The reduction formula for the integral of the n-th power of the sine function. Now, whilst this formula is valid for any value of integer n greater than or equal to 1 (i.e. natural numbers), it is …

2024年12月16日 · Misc 30 Find the derivative of the following functions (it is to be understood that a, b, c, d, p, q, r and s are fixed non-zero constants and m and n are integers): 𝑥/(𝑠𝑖𝑛𝑛 𝑥) Let f(x) = 𝑥/(𝑠𝑖𝑛𝑛 𝑥) …

In basic trigonometry computes sine, cosine, tangent, and their reciprocal. Calculates arcsin, arccos, and arctan values inside inverse trigonometric equations. Trigonometric identities …

To see how to prove this, let us come up with some sequence (x_n)_n such that f_n(x_n) does not converge to 0. Below, I describe in detail ... x^2\sin(x) continuous using \epsilon\delta method

I am working on trying to solve this problem: Prove: $\int \sin^n{x} \ dx = -\frac{1}{n} \cos{x} \cdot \sin^{n - 1}{x} + \frac{n - 1}{n} \int \sin^{n - 2}{x} \ dx$ Here are the steps that I fol...

In this wiki, we'll generalize the expansions of various trigonometric functions. We have the following general formulas: \cos (n\theta) + i\sin (n\theta) = \big (\cos (\theta) + i\sin (\theta) …

We can use the reduction formulas to integrate any positive power of sin x or cos x.

To solve a trigonometric simplify the equation using trigonometric identities. Then, write the equation in a standard form, and isolate the variable using algebraic manipulation to solve for …

I currently try to prove the following equation: $$(\sin(x))^n=\sum_{k=0}^{n}{a_k\cos(kx)+b_k\sin(kx)}$$ with $a_0,...,a_k$ and $b_0,...b_k$ …

2019年11月5日 · \(I_n = -\frac{1}{n}sin^{n-1}x\,cos\,x+ \frac{(n-1)}{n} \int \,sin^ {n-2}x\,dx\) Hence, \(\int\,sin^nx\,dx = -\frac{1}{n}sin^{n-1}x\,cos\,x+ \frac{(n-1)}{n} \int \,sin^ {n-2} x\,dx.\)