Question

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

Answer 1

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)

∴ $sin(x+\frac{\pi}{2})=cos(x)$

- Vice versa

- 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)

∴ $cos(x-\frac{\pi}{2})=sin(x))$

- Look to the attached graphs for more understand