sinusoidal function

Question

y = V + A sin C (x − D)

a.Find the upper bound and lower bound of the function if V = −2 and A =11/2

b.Find the period of the function if C = π / 14

show work please

Answer 1

a) The function is translated vertically by V and the amplitude is A, so we have:

upper bound = V + A = -2 + 11/2 = 7/2

lower bound = V - A = -2 - 11/2 = -15/2

b) The period of the sinusoid is 2π/C, or:

2π / (π / 14) = 28

Answer 2

a.

Center line at y = -2

Amplitude is 2|A| = 11

Upper bound -2 + 11

Lowe bound -2 - 11

b.

Period = 2π / |C|

Perriod = 2π / (π / 14)