Seven years ago, douglas purchased a $204,000 home with a 30-year mortgage at 4.5%. having recently lost his job, he can no longer afford to make his mortgage payments. if he currently owes $177,533.62 and his lender offered to extend the loan by 7 years at 4.25%, what will be his new mortgage payment?

The parent cosine function can be transformed and translated. So, from the basic function cos(x) we can obtain function acos(bx+c). In our case, a=3- amplitude, b=10- the period change and c=-pi- the phase shift. So, the parent cosine function is mutiplied with 3 (which gives the amplitude of the function, 3*0.5=1.5). The period of the function is changed, and is 2pi/b=2pi/10=pi/5 and the cos(x) is phase shifted for c/b=-pi/10.