Find the period and phase shift of y tan pix pi4 and sketc

Find the period and phase shift of y = tan (pix + pi/4) and sketch its graph. The beam from an island light house completes one rotation every two minutes. At time t (in minutes), the distance d (in miles) between the closest point on shore to the island and the light on the shoreline is given by d(t) = 3 tan(pi t). Find d(0.15), d(0.25) and d(0.45). What happens to the distance d as t approaches 1/2?

Solution

y = tan ( pi x + pi/4 )

standard equation of tan function is given by

y = A tan ( Bx + C ) + D

where, A is amplitude

period is pi/ B

phase shift = -C/B

therefore, compring our problem equation with standard equation

we get period = pi / pi = 1

phase shift = - pi/4 / pi = -1/4