How do you write the equation of the sine function with an amplitude of 4, a period of pi/2 and a phase shift of - pi/4?

1 Answer
Jim G.
Jun 12, 2016

#y=4sin(4x+pi)#

Explanation:

The standard form of the #color(blue)"sine wave function"# is

#color(red)(|bar(ul(color(white)(a/a)color(black)(y=asin(bx+c)+d)color(white)(a/a)|)))#

where amplitude = |a| , period #=(2pi)/b#

c is the phase shift and d , the vertical shift

here a = 4 , b#=(2pi)/(pi/2)=4 #

phase shift #=-c/brArrc=pi#

Substitute these values into standard form

#rArry=4sin(4x+pi)" is the equation"#

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