The sine function undergoes a vertical translation of 4 units down and a phase shift of 45 degrees to the right. what is the equation of the resulting function?

1 Answer
Ayush S.
May 28, 2018

#sin(x-pi/4)-4#

Explanation:

for#" sine"# or #"cosine"# function always remember the general form. #asin(bx+-c)+-d " /acos(bx+c)"+-d"#

here #a# is the amplitude(or the heights above or below the origin)
#b# is the extent of shrinking or expanding
"#c# is the phase (can also be considered horizontal shift)"
"#d# is the vertical shift"

from the question ,we have vertical translation of 4 units down(implying negative vertical shift)
and phase change(or horizontal translation) is of #45^0" "i.e" "pi/4 # units implying negative horizontal shift(actually it is opposite of vertical shift trend)

then the function will be
#asin(bx-pi/4)-4#
now assuming #a=1,b=1#(as it is not stated explicitly)
the function is
#sin(x-pi/4)-4#

it will be more clear from graph
graph{sin(x-pi/4)-4 [-10, 10, -5, 5]}

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