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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 \(g(x) = \cos x\)?

 Jul 28, 2020
 #1
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Is it in radians or degrees?

 Jul 28, 2020
 #2
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it's in radians

Guest Jul 28, 2020
 #3
avatar+111112 
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\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)

 Jul 28, 2020
edited by Melody  Jul 28, 2020
 #4
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thank you so much! :)

Guest Jul 28, 2020

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