Trigonometric identities

[nenerufus]

Can you help me show how the graphs are the same by using the trigonometric identities which pertains to this question: Which of the following represent the same graph? Check your results analytically using trigonometric identities.

(a) y=sin (x+pie/2) (b) y=cos (x + pie/2)
(c) y=-sin (x + pie) (d) y=cos (x - pie)
(e) y=-sin (pie - x) (f) y=cos (x - pie/2)
(g) y=-cos (pie -x) (h) y=sin (x - pie/2)

The graphs that are alike are (a,g), (b,e), (c,f), (d,h).

 

[tkhunny]

You can expand them all with sum identities:

sin(a+b) = sin(a)*cos(b)+cos(a)*sin(b)
cos(a-b) = cos(a)*cos(b)+sin(a)*sin(b)
sin(a-b) = sin(a)*cos(b)-cos(a)*sin(b)
cos(a+b) = cos(a)*cos(b)-sin(a)*sin(b)

By the way, "pie" is for eating, "pi" is the number.