For how many values of n with \(0\le n\le 100\) is the graph of \(f(x) = \sin \left(x + n\right)\) identical to the graph of \(g(x) = \cos x\)?
+118667 \text{For how many values of n with } 0\le n\le 100 \text{ is the graph of} f(x) = \sin \left(x + n\right) \text{ identical to the graph of } g(x) = \cos x?
\(\text{For how many values of n with } 0\le n\le 100 \text{ is the graph of}\\ f(x) = \sin \left(x + n\right) \text{ identical to the graph of } g(x) = \cos x? \)
\( 0\le n\le 100 \\ 0\le n\le 31.83\pi \\ \)
\(sin0=cos(0+\pi/2)\quad \text{then it will work every 2pi after that}\\ n=\frac{\pi}{2},\;\;\frac{5\pi}{2},\;\;\frac{9\pi}{2},\;\;.....\frac{61\pi}{2}\\ 1,5,9,4c-3, 4*16-3\\ \text{so that appears to be 16 times.} \)
Here is the graph
https://www.desmos.com/calculator/ybf8ktq9km
(I do admit that this is not the best of algebraic answers)
