SOLUTION: Will sin(x) ever equal cos(x)? I do not need solutions. Also, does sin(x) = cos(x - {{{pi}}}/2)? Explain.

Algebra ->  Trigonometry-basics -> SOLUTION: Will sin(x) ever equal cos(x)? I do not need solutions. Also, does sin(x) = cos(x - {{{pi}}}/2)? Explain.      Log On


   

Question 49322: Will sin(x) ever equal cos(x)? I do not need solutions. Also, does sin(x) = cos(x - pi/2)? Explain.
Answer by Nate(3500) About Me  (Show Source):
You can put this solution on YOUR website!
Yes, sin(x) will equal cos(x) eventually:
graph%28600%2C200%2C-10%2C10%2C-1%2C1%2Csin%28x%29%2Ccos%28x%29%29
Does sin(x) = cos(x - pi/2) .... Yes
Remember: sin(x - 1) shifts horizontally -c units
sin(pi/2) = 0
cos(0) = 0
So, sine is pi/2 to the right of cosine.
Cos(x - pi/2):
graph%28600%2C200%2C-10%2C10%2C-1%2C1%2Ccos%28x+-+1.570796327%29%29
Sin(x):
graph%28600%2C200%2C-10%2C10%2C-1%2C1%2Csin%28x%29%29