Question

Part 2: Using these similarities and differences, how would you transform f(x) = 2 sin(2x - π) + 3 into a cosine function in the form f(x) = a cos(bx - c) + d?

Answer 1

@phi

Answer 2

any thoughts?

Answer 3

Part 1: Using complete sentences, compare the key features and graphs of sine and cosine. What are their similarities and differences?

The graph of cosine and sine are pretty much the same except that the graph of cosine is shifted by pi / 2 behind the sine graph.

I did that for part 1

Answer 4

for part 2, both sin and cos have the same shapes (just shifted), so the numbers on the outside should match up. i.e. the a and d

Answer 5

cosine is just shifted from sine?
im guessing we will use pi/2

Answer 6

and we need to combine the function somehow but im not quite sure what to plug in

Answer 7

first a=2 and d is 3

Answer 8

next we know sin(x) = cos(x-π/2)
to make it clearer (maybe). call 2x - π = A
sin(A) = cos(A - π/2)
now replace A with 2x-π
sin(2x - π) = cos(2x-π - π/2)

Answer 9

ok i understand all of that, what would be next? simplify that?

Answer 10

I would simplify -pi - pi/2 to be -2pi/2 - pi/2 = -3pi/2
so you get
sin(2x - π) = cos(2x-3π/2 )

Answer 11

as a check , see
http://www.wolframalpha.com/input/?i=plot+sin%282x+-+%CF%80%29+and+cos%282x-3%CF%80%2F2+%29

Answer 12

ok i understand how you simplified

Answer 13

now match
cos(bx - c) with cos(2x-3π/2 )

Answer 14

b is 2
and c is 3pi/2

Answer 15

cos(2x - 3pi /2)
they're the same?

Answer 16

?

Answer 17

the final result is
f(x) = 2 sin(2x - π) + 3
becomes
f(x) = 2 cos(2x - 3π/2) + 3?

Answer 18

this is confusing
do i use the full formula then? f(x) = a cos(bx - c) + d
2cos(2x - 3pi/2) +3?

Answer 19

okay i'll try to sum all of this up, was part 1 right? up near the top

Answer 20

they want to rewrite
2 sin(2x - π) + 3
using cosine instead of sine

we know sin(A)= cos(A - π/2)
so we "snip out" sin(2x - π) and put in cos(2x - π - π/2) instead:
2 cos(2x - π - π/2)+ 3

and simplify the "inside" part to get
2 cos(2x - 3π/2)+ 3

Answer 21

wow thanks once again, i couldn't do this without you haha. i have a couple more if you wouldn't mind going over

Answer 22

what I wrote is confusing. better is the cosine is the sin curve shifted to the left pi/2 radians

Answer 23

I have to sign off for now.

Answer 24

okay thanks for the help!