Respuesta :
Recall that the general formula of a cosine function is of the form
[tex]A\cdot\cos (Bx-C)+D[/tex]where A is the amplitude, D is the midline, the number C/B is the phase shift and the number 2*pi/B is the period.
We are told that A=3 and D=5. Also, we are told that the period is pi/2. Since we don't have any information regarding the phase shift, we will asume that the phase shift is 0. Then we have the following equations:
[tex]\frac{C}{B}=0[/tex]and
[tex]\frac{2\cdot\pi}{B}=\frac{\pi}{2}[/tex]From the first equation we deduce that C should be zero. From the second equation by multiplying by B on both sides and dividing by pi on both sides, we get
[tex]2=\frac{B}{2}[/tex]If we multiply by 2 on both sides, we get
[tex]B=2\cdot2=4[/tex]so gathering our previous results, we get the formula
[tex]3\cos (4x)+5[/tex]