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I was asked to find a formula for $\sin(5x)$ in terms of $\sin(x)$ and $\cos(x)$. I thought about using euler formula which gives: $$\sin(5x) = e^{i\sin(5x)} = \cos(\sin(5x))+i\cdot sin(\sin(5x))$$...

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Use the form asin(bx−c)+ d a sin (b x - c) + d to find the variables used to find the amplitude, period, phase shift, and vertical shift. Find the amplitude |a| | a |. Find the period of sin(5x) sin …

A good method to expand sin(5x) is by using De Moivre's theorem (r(cos(x) + i ⋅ sin(x))n = rn(cos(nx) + i ⋅ sin(nx))). When r = 1, cos(nx) + i ⋅ sin(nx) = (cos(x) + i ⋅ sin(x))n. cos(nx) + i ⋅ …

What is the general solution for sin (5x)=1 ?

What is the general solution for sin (5x)=sin (x) ?

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Mar 15, 2016 · Suppose $\sin x=\sin y$. Then for the cosine there are just two possibilities, since $\cos^2x=1-\sin^2x=1-\sin^2y=\cos^2y$: either $\cos x=\cos y$ or $\cos x=-\cos y$.