Please help Find a possible formula of the form A sin t k o

Find a possible formula of the form A sin t + k or A cos t + k for the periodic function with midline y = 7, amplitude 6 with a minimum value at t = 0.

Solution

g(t) = Asin(t+c) +k where c is phase shift

midline =7

ampltude = 6

minimum value = = 7 -6 = 1

g(t) = 1 ; 1 = 6sin(t+c) +7

-6 = 6sin(t+c) ;

-1 = sin(c)

c = 3pi/2

So, g(t) = 6sin(t+3pi/2) + 7