Find a possible formula of the form Sx a sinx k or Cx aco

Find a possible formula of the form S(x) = a sin(x) + k or C(x) = acos(x) + for each of the following periodic functions The function f(x) has midline y = 5 amplitude 2 and maximum value at t = 0 f(x) = The function g(x)has midline y = - 2 and has minimum value -12 at x = 3 pi/2 g(x) =

Solution

a. midline y=5 means vertical shift of +5 to the cosx graph

Amplitude = 2 so, in acosx +k ; a=2.So, y = 2cosx +5 as max. value is

at x =0.Therefore we choose a cos function instead os sin:

f(x) = 5 +2cosx

b) Max value at x= 3pi/2 , so we can assume sin function.

Midline y =-2 , vertical shift down of 2 units

y = -2 + asinx

max. value = -12.So, -12 = -2- a*1

a = 10

So, f(x) = -2 + 10sinx