Folks, how can $\sin^4 (x)$ be simplified to a trig function with power of 1? I tried: $ (\sin^2 (x))^2 = ( (1-\cos2x)/2)^2$ but still getting $\cos x$ to the power of $2$.

Trigonometry is a branch of mathematics that deals with the relationships between the sides and angles of triangles. It uses functions such as sine, cosine, and tangent to describe the ratios of …

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2024年12月16日 · Ex 7.3, 10 Integrate the function 𝑠𝑖𝑛4 𝑥 ∫1 sin^4⁡𝑥 𝑑𝑥 =∫1 (sin^2⁡𝑥 )^2 𝑑𝑥 =∫1 ((1 − cos⁡2𝑥)/2)^2 𝑑𝑥 =1/4 ∫1 (1−cos⁡2𝑥 )^2 𝑑𝑥 We know that 𝑐𝑜𝑠⁡2𝜃=1−2 〖𝑠𝑖𝑛〗^2⁡𝜃 2 〖𝑠𝑖𝑛〗^2⁡𝜃=1−𝑐𝑜𝑠⁡2𝜃 〖𝑠𝑖𝑛〗^2⁡𝜃=(1 − 𝑐𝑜𝑠⁡2𝜃)/2 Replace 𝜃 by 𝑥 ...

how can I find the period of f = sin4(x)? If T is a period of \sin^4 {x}, then \forall x \in \mathbb {R} \sin^4 { (x+T)}-\sin^4 {x}=0 ,\\ (\sin^2 { (x+T)}-\sin^2 {x}) (\sin^2 { (x+T)}+\sin^2 {x})=0,\\ \dfrac {1-\cos (2 (x+T))} {2}-\dfrac {1-\cos (2x)} {2}=0, \\ \cos (2x)-\cos { (2 (x+T))}=0,\\ …

2018年3月11日 · I cannot prove the $\sin^4 (x)$ identity using $z= cis (x)$. I know that you have to use de Moivre's theorem and compare the real values of $z^4$ but I am stuck at this step: $$\sin^4 (x)= -\cos^4 (x) ...

how to represent sin4(x) sin 4 (x) by Fourier series? Obviously, sin4(x) sin 4 (x) is an even function, so bn = 0 b n = 0. How can i get an a n ?

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 …

Here, we show you a step-by-step solved example of simplify trigonometric expressions. This solution was automatically generated by our smart calculator: $\frac {1-sin\left (x\right)^2} {csc\left (x\right)^2-1}$ Applying the trigonometric identity: $\csc\left …

The calculator will find the integral/antiderivative of sin (x)^4, with steps shown.