Lesson 17 - Sinusoidal Functions

Pg. 235: 3,4,5,8,10,11,17,21,23,26,27

Answer Only

Lesson 17 - 6.1 #3 State of Graph of a step function is periodic:

Yes (repeats every 2)

Lesson 17 - 6.1 #4 State of Graph of a step function is periodic:

Yes (repeats every period)

Lesson 17 - 6.1 #5 State of Graph of a step function is periodic:

No (rises and fall with any repeats horizontal)

Lesson 17 - 6.1 #8 State of Graph of a step function is periodic:

No (no consistent horizontal repeats)

Lesson 17 - 6.1 #10 State period from table of value:

Period, p = 40 (41 - 1 and 81 - 41, goes from 5 to 5)

Lesson 17 - 6.1 #11 State period from graph of cos(x) function:

Period, p = 4 (max to max, 4 - 0)

Lesson 17 - 6.1 #17 Study of Ferris wheel movement of dia 20 m.

Max. = 24, Min = 4, and period = 2

So D = 14 and A = 10

Formula is

Lesson 17 - 6.1 #21 State period and time of ride or 2.75 cycle given the period in min:

Note

So 2.75 cycles take 4(2.75) = 11 min.

Lesson 17 - 6.1 #23 Oscillation of spring from ceiling problem:

Max. = 14, Min = 6 so D = 10 and A = 4.

The period, p = 1 sec

So spring oscillates from lowest to highest point in 0.5 seconds.

Lesson 17 - 6.1 #26 Comparing spring oscillation of two springs from a ceiling given their graphs:

Graph A: and

Graph B:

(a) B is closest to ceiling when not in used since D = 10

(b) A makes the largest oscillation since A = 10

(c) A makes the fastest oscillation since 4 oscillations in same period as B.

Lesson 17 - 6.1 #27 Sketch graph of periodic function given:

Min = 30 deg C

Max. = 110 deg C

Lowest point when t = 0

P = 5 hours (time for 1 cycle)