Determine the number of cycles the following sine function has in the interval from 0 to 2pi. Find the amplitude and period of the function. y equals negative 4 sine pi theta.

Answer 1

y = -4sin(piT)

coefficient of T= 2pi/B where B = period

pi = 2pi/B

1 = 2/B

B = 2

number of cycles from 0 to 2pi = the coefficient of T = pi

Amplitude = the Absolute value of the coefficient of the sine term = 4

= half of (max - min) = (1/2)(4 - -4 ) = 8/2= 4

Answer 2

y = -4sin(πΘ)

The amplitude is 4.

To find the period, period = 2π/B The B term is π.

period = 2π/π

period = 2