Which of the following could be the equation of the function below?

Asked by wiki @ 29/10/2020 in Mathematics viewed by 301 People

Answered by wiki @ 29/10/2020

Answer. Second option: y=0.5 cos (4(x+pi/2))-2

Solution:

y=a cos (b(x+c))+d

ymax=-1.5; y min=-2.5

d=(ymax+ymin)/2

d=(-1.5+(-2.5))/2

d=(-1.5-2.5)/2

d=(-4.0)/2

d=-2.0

The horizontal axis is y=-2→d=-2

y= a cos(b(x+c))+(-2)

y=a cos (b(x+c))-2

The amplitude (a) is:

a=ymax-d=d-ymin

a=-1.5-(-2)=-2-(-2.5)

a=-1.5+2=-2+2.5

a=0.5=0.5

The period is Pi/2 because in Pi units the graph repeats twice:

Period: P=Pi/2

P=2Pi/b

Replacing P by Pi/2 in the formula above:

Pi/2=2Pi/b

Solving for b: Multiplying both sides of the equation by 2b:

2b(Pi/2)=2b(2Pi/b)

Pi b=4 Pi

Dividing both sides of the equation by Pi:

(Pi b)/Pi=(4 Pi)/Pi

b=4

y=0.5 cos (4(x+c))-2

We can say that the graph is translated Pi/2 units to the left, then c=Pi/2

y=0.5 cos (4(x+pi/2))-2

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