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

8 answers

trig identity:
sin theta = cos (pi/2-theta)
so
y = 3 sin (4x-pi) + 4
but from above trig identity
y = 3 cos [ pi/2 - (4x-pi) ] + 4
or
y = 3 cos (-4x + 3 pi/2) + 4
but
cos (- theta) = cos theta
so
y = 3 cos (4x-3 pi/2) + 4

Thank you

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

You are welcome :)

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

3-x/(x+3)(x-3)

is this right?

this helped me a lot