Interactive practice questions
In Valera, the average monthly rainfall is recorded.
Plot the average monthly rainfall over a two-year period, letting $x=1$x=1 correspond to January of the first year.
| Month | Rainfall (cm) | Month | Rainfall (cm) |
|---|---|---|---|
| Jan | $1.5$1.5 | July | $11.5$11.5 |
| Feb | $1.5$1.5 | Aug | $12.5$12.5 |
| Mar | $3.5$3.5 | Sept | $11$11 |
| Apr | $7$7 | Oct | $7.5$7.5 |
| May | $9.5$9.5 | Nov | $4.5$4.5 |
| June | $11.5$11.5 | Dec | $2$2 |
The highest average monthly rainfall is $12.5$12.5 cm, and the lowest average monthly rainfall is $1.5$1.5 cm. Their average is $7$7 cm. The line that represents the average annual temperature is graphed below. What is the equation of this line?
The average rainfall can be approximated using a sine wave. Which curve best approximates the average rainfall in Valera? Use your graph from the previous questions to help you.
Use your answer from part (c) to complete the statement:
The sine curve that best approximates the average monthly rainfall has an amplitude of $\editable{}$ cm, a period of $\editable{}$ months, and a phase shift of $\editable{}$ months.
Determine the equation of the graph given that it is of the form $y=\sin\left(x+c\right)+d$y=sin(x+c)+d, where $c$c is the least positive value and $x$x is in radians.
Determine the equation of the graphed function given that it is of the form $y=\cos\left(x-c\right)$y=cos(x−c), where $c$c is the least positive value.
Determine the equation of the graph given that it is of the form $y=a\cos\left(x-c\right)$y=acos(x−c), where $c$c is the least positive value and $x$x is in radians.