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1.05 Applications of trigonometric functions

Interactive practice questions

In Valera, the average monthly rainfall is recorded.

a

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
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b

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?

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c

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.

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A

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B

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C

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D
d

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.

Hard
15min

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.

Easy
2min

Determine the equation of the graphed function given that it is of the form $y=\cos\left(x-c\right)$y=cos(xc), where $c$c is the least positive value.

Easy
1min

Determine the equation of the graph given that it is of the form $y=a\cos\left(x-c\right)$y=acos(xc), where $c$c is the least positive value and $x$x is in radians.

Easy
1min
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Outcomes

3.2.3.2

identify contexts suitable for modelling by trigonometric functions and their derivatives and use the model to solve practical problems; verify and evaluate the usefulness of the model using qualitative statements and quantitative analysis

3.2.3.3

use trigonometric functions and their derivatives to solve practical problems; including trigonometric functions of the form 𝑦 = sin(𝑓(𝑥)) and 𝑦 = cos(𝑓(𝑥)).

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