Question

32. Graph the following functions over 2 CYCLES Label the aves [C, 20m] a) y- sinx+60)-3 Amplitude, Maximum Minimum Period (one cycle). Vertical Translation b) y-3 sin [20x-30]-2 Period (one cycle) Amplitude, -Phase shift Maximum- Vertical Translation Minimum

Answer 1

The graph of the (a) is as follows:

In general y = d + a sin (bx - c) where a-amplitude d-baseline period: 2 pi/b phase shift = c/b y = sin (x + 60 degree) - 3 therefore compare it wit y = a sin (bx - c) + d a = 1, b = 1, c = -60 degree, d = -3. Amplitude = 1Period = 2 pi/b = 2 pi. From the graph maximum value is -2 and minimum value is -4 phase shift = c/b = -60/1 = -pi/3 phase shift is negative. It indicater shifting to the left. Therefore Amplitude 8implies 1 period implies 2 pi Maximum -2 Minimum implies -4 phase shift implies pi/3 shiftingf to left.y = 3 sin (2(x - 30 degree)) - 2 y = 3 sin (2x - 60 degree) - 2 compare with y = a sin (bx - c) + d a = 3, b = 2, c = pi/3, d = -2
for part(b)  

Graph is: