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

y = sin(4x) + 3

Explanation:

y = Asin(Bx + C) + D

A is amplitude = 1

B = 2pi/period = 2pi / (pi/2) = 4

C does not mention.

D: shift up or down = 3

=> y = sin(4x) + 3

Answer 2

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