Trigonometric Functions

Question

For each item below, sketch the graph of the given equation and identify its (a) amplitude, (b) period, (c) horizontal shift, and (d) vertical shift. PROVIDE FULL SOLUTION.

1) 

2) 

Answer 1

y=Asin(B(x+C))+D

A is amplitude, 2pi/B = period, C is horizontal shift, D is vertical shift

for 1) A= 3, 2pi/(2/3) = 3pi = period, B=2/3

C=-3pi/4 divided by 2/3 = -3pi/4 x 3/2 = -9pi/8

D = -2

for 2) A=2, 2pi/5= period, B=5

C=4pi/3 divided by 5 = 4pi/15

D = 3