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The average daily temperature, t, in degrees fahrenheit for a city as a function of the month of the year, m, can be modeled by the equation graphed below, where m = 0 represents january 1, m = 1 represents february 1, m = 2 represents march 1, and so on. if the equation is t = a cosine (startfraction pi over 6 endfraction (m 1)) k, what are the values of a and k?

Sagot :

abidemiokin

The equivalent expression for the function is given as [tex]t=-35sin(\frac{\pi}{6}m +55)\\[/tex]

Sine and cosine functions

Given the average daily temperature of a city expressed acccording to the cosine function

[tex]t=35cos(\frac{\pi}{6} (m+3))+55[/tex]

In order to rewrite as a function of sine, first expand the parenthesis to have:

[tex]t=35cos(\frac{\pi}{6}m +3(\frac{\pi}{6} ))+55\\t=35cos(\frac{\pi}{6}m +\frac{\pi}{2} )+55\\[/tex]

Recall from trigonometry identity that:

cos(x+90⁰)=-sin(x)

The equivalent expression for the function is given as:

[tex]t=-35sin(\frac{\pi}{6}m +55)\\[/tex]

Learn more on trigonometry functions here: https://brainly.com/question/1143565

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View image abidemiokin

Answer:

A

Step-by-step explanation:

t--35 sin(m) + +55

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