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