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Nataly_w [17]
3 years ago
13

Can you rewrite a sine as a cosine function and vice versa when describing a general sinusoidal graph? Explain.

Mathematics
1 answer:
MatroZZZ [7]3 years ago
4 0

Answer:

sin(x+\frac{\pi}{2})=cos(x)

cos(x-\frac{\pi}{2})=sin(x)

Step-by-step explanation:

* Lets explain how to solve the problem

- We can write a sine as a cosine by translate the sine function to the

 left by \frac{\pi}{2}

- sin(x+\frac{\pi}{2})=cos(x)

∵ The value of sin(0 + π/2) = 1

∵ cos(0) = 1

∴ sin(0 + π/2) = cos(0)

∴ If sin(x) translated to the left by \frac{\pi}{2}, then it will be

  cos(x)

∴ sin(x+\frac{\pi}{2})=cos(x)

- <u><em>Vice versa</em></u>

- We can write a cosine as a sine by translate the cosine function to

 the right by \frac{\pi}{2}

- cos(x-\frac{\pi}{2})=sin(x)

∵ The value of cos(0 - π/2) = 0

∵ sin(0) = 0

∴ cos(0 - π/2) = sin(0)

∴ If cos(x) translated to the right by \frac{\pi}{2}, then it will be

  sin(x)

∴ cos(x-\frac{\pi}{2})=sin(x))

- <em>Look to the attached graphs for more understand</em>

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