Posted by Man on .
Part 1: Using complete sentences, compare the key features and graphs of sine and cosine. What are their similarities and differences?
Answer: The sine graph will always pass through (0, 0), While the cosine graph wouldn't. If the graph is 2cosx, it will pass through (0, 2). How high the graphs go depend on its amplitude, (how high or how far the graphs go can sometimes be infinite).
Part 2: Using these similarities and differences, how would you transform f(x) = 3 sin(4x  π) + 4 into a cosine function in the form f(x) = a cos(bx  c) + d?
Answer: I don't know, please help

Algebra II 
Damon,
trig identity:
sin theta = cos (pi/2theta)
so
y = 3 sin (4xpi) + 4
but from above trig identity
y = 3 cos [ pi/2  (4xpi) ] + 4
or
y = 3 cos (4x + 3 pi/2) + 4
but
cos ( theta) = cos theta
so
y = 3 cos (4x3 pi/2) + 4 
Algebra II 
Man,
Thank you

Algebra II 
Damon,
also in your explanation explain that the cosine curve is 90 degrees or pi/2 radians behind the sine curve if you graph y = sin theta and y = cos theta versus theta

Algebra II 
Damon,
You are welcome :)

Algebra II 
Damon,
By the way, there are an infinite number of solutions. eg 3 cos (4x  7 pi/2)+4
or
 3 cos(4x pi/2) + 4
etc 
Algebra II 
debra,
3x/(x+3)(x3)

Algebra II 
Isabella,
is this right?

Algebra II 
khloyie,
this helped me a lot