How do you write an equation of a cosine function with Amplitude=2.4, Period=0.2, Phase Shift=pi/3, and Vertical shift=.2?

1 Answer
Mar 30, 2018

Answer:

#y=12/5cos(10pix-(10pi^2)/3)+1/5#

Explanation:

Trigonometric functions can be expressed in the form:

#y=acos(bx+c)+d#

Where:

# \ \ \bba \ \ \ \ \ \ \ \ \# is the amplitude.

#bb((2pi)/b) \ \ \ \ \ \ # is the period. *

#bb((-c)/b) \ \ \ \ \ \ # is the phase shift.

# \ \ \ bbd \ \ \ \ \ \ \ \ \# is the vertical shift.

(where #2pi# is the normal period of the cosine function ) *

We require:

#a=2.4=12/5#

Period of #0.2=1/5#

#:.#

#(2pi)/b=1/5#

#b=10pi#

Phase shift of #pi/3#

#(-c)/(10pi)=pi/3#

#c=-(10pi^2)/3#

Vertical shift of #0.2=1/5#

#d=1/5#

#:.#

#y=12/5cos(10pix-(10pi^2)/3)+1/5#