+0

# HELP!

0
70
4

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
+111112
-1

Is it in radians or degrees?

Jul 28, 2020
#2
0

Guest Jul 28, 2020
#3
+111112
+1

\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
+1

thank you so much! :)

Guest Jul 28, 2020