Exam 27: Graphs of Sine and Cosine Functions

For a person at rest,the velocity v (in liters per second)of airflow during a respiratory cycle (the time from the beginning of one breath to the beginning of the next)is given by​ $v = 0.85 \sin \left( \frac { \pi t } { 3 } \right)$ , ​ Where t is the time (in seconds). (Inhalation occurs when v > 0 and exhalation occurs when v < 0. ) ​ Find the number of cycles per minute. ​

The daily consumption C (in gallons)of diesel fuel on a farm is modeled by​ $C = 30.4 + 21.6 \sin \left( \frac { 2 \pi t } { 365 } + 10.2 \right)$ , ​ Where t is the time (in days),with t = 1 corresponding to January 1. What is the average daily fuel consumption? ​

Find the period and amplitude. ​ Y = -7 sin x ​

Determine which of the graphs below represents the following function y=|x|sin x ​

The daily consumption C (in gallons)of diesel fuel on a farm is modeled by​ $C = 30.8 + 21.6 \sin \left( \frac { 2 \pi t } { 365 } + 10.9 \right)$ , ​ Where t is the time (in days),with t = 1 corresponding to January 1. What is the period of the model? ​

​Determine the period and amplitude of the following function​ $y = 3 \cos \left( \frac { 2 x } { 3 } - \frac { 1 } { 6 } \right)$ ​

After exercising for a few minutes,a person has a respiratory cycle for which the velocity of airflow is approximated by​ $v = 1.75 \sin \left( \frac { \pi t } { 3 } \right)$ , ​ Where t is the time (in seconds). (Inhalation occurs when v > 0 and exhalation occurs when v < 0. ) ​ Find the number of cycles per minute. ​

Write an equation for the function that is described by the given characteristics. ​ A sine curve with a period of 4π,an amplitude of 4,a left phase shift of $\frac { \pi } { 4 }$ ,and a vertical translation down 5 units. ​

Select the graph of the function.(Include two full periods. )​ $y = 4 + \frac { 1 } { 10 } \cos 60 \pi x$ ​

After exercising for a few minutes,a person has a respiratory cycle for which the velocity of airflow is approximated by​ $v = 1.75 \sin \left( \frac { \pi t } { 3 } \right)$ , ​ Where t is the time (in seconds). (Inhalation occurs when v > 0 and exhalation occurs when v < 0. ) Select the graph of this velocity function.

Select the graph of the function.(Include two full periods. )​ $y = - \sin \frac { 8 \pi x } { 3 }$ ​

Use a graphing utility to select the graph of the function.Include two full periods. $y = - 2 \sin \left( \frac { 8 } { 3 } x - \frac { \pi } { 3 } \right)$ ​

Select the graph of the function.(Include two full periods. )​ $y = 2 - \sin \frac { 2 \pi x } { 3 }$ ​

Find the period and amplitude.​ $y = \frac { 4 } { 5 } \sin 2 \pi x$ ​

Use a graphing utility to select the graph of the function.Include two full periods.​ $y = \frac { 1 } { 100 } \sin 110 \pi t$ ​

Select the graph of the function.(Include two full periods. ) ​ Y = sin 2x ​

​Determine the period and amplitude of the following function​ $y = 5 \cos \left( \frac { 5 x } { 7 } + \frac { 1 } { 3 } \right)$ ​

Write an equation for the function that is described by the given characteristics. ​ A sine curve with a period of π,an amplitude of 4,a right phase shift of $\frac { \pi } { 2 }$ ,and a vertical translation up 7 units. ​

Sketch the graph of the function below,being sure to include at least two full periods. ​ Y = - cos(x+ $\frac { \pi } { 2 }$ ) ​

Write an equation for the function that is described by the given characteristics. ​ A cosine curve with a period of 4π,an amplitude of 7,a right phase shift of $\frac { \pi } { 2 }$ ,and a vertical translation up 2 units. ​