Question

Complete the general form of the equation of a sinusoidal function having an amplitude of 1, a period of pi/2 , and a vertical shift up 3 units.

Answer 1

Sinusoidal equations are trigonometric functions involving sine and cosine functions. Graphically, they look like wave patterns having amplitudes and periods. The general form of a sinusoidal equation is 

y = A sin(Bx + C) + D

where

A = amplitude
B = frequency
C = shift on starting angle
D = shift of wave on the y-axis

From the given problem, A = 1 and D = 3. There is no value for C because there is no mention of any shift in angle. About the frequency, you can obtain this by getting the reciprocal of the period. Thus, B = 2/π. The complete equation is

y = sin(2x/π) + 3