Answer:
[tex]sin(x+\frac{\pi}{2})=cos(x)[/tex]
[tex]cos(x-\frac{\pi}{2})=sin(x)[/tex]
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 [tex]\frac{\pi}{2}[/tex]
- [tex]sin(x+\frac{\pi}{2})=cos(x)[/tex]
∵ 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 [tex]\frac{\pi}{2}[/tex], then it will be
cos(x)
∴ [tex]sin(x+\frac{\pi}{2})=cos(x)[/tex]
- Vice versa
- We can write a cosine as a sine by translate the cosine function to
the right by [tex]\frac{\pi}{2}[/tex]
- [tex]cos(x-\frac{\pi}{2})=sin(x)[/tex]
∵ 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 [tex]\frac{\pi}{2}[/tex], then it will be
sin(x)
∴ [tex]cos(x-\frac{\pi}{2})=sin(x))[/tex]
- Look to the attached graphs for more understand
