Posted by Man on Sunday, May 25, 2014 at 7:05pm.
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, Sunday, May 25, 2014 at 7:16pm
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, Sunday, May 25, 2014 at 7:18pm
Thank you

Algebra II  Damon, Sunday, May 25, 2014 at 7:22pm
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, Sunday, May 25, 2014 at 7:22pm
You are welcome :)

Algebra II  Damon, Sunday, May 25, 2014 at 7:33pm
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, Sunday, May 25, 2014 at 10:44pm
3x/(x+3)(x3)

Algebra II  Isabella, Wednesday, June 3, 2015 at 7:48pm
is this right?

Algebra II  khloyie, Wednesday, June 3, 2015 at 7:59pm
this helped me a lot
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