Temperature The maximum afternoon temperature degrees...

Temperature The maximum afternoon temperature degrees Fahrenheit) in a given city is approximated by $$T(t)=60-30 \cos (t / 2)$$ where $t$ represents the month, with $t=0$ representing January, $t=1$ representing February, and so on. Use a calculator to find the maximum afternoon temperature for the following months. (a) Februry $\quad$ (b) April $\quad$ (c) September (d) July (e) December

Temperature The maximum afternoon temperature degrees Fahrenheit) in a given city is approximated by
$$T(t)=60-30 \cos (t / 2)$$
where $t$ represents the month, with $t=0$ representing January, $t=1$ representing February, and so on. Use a calculator to find the maximum afternoon temperature for the following months.
(a) Februry $\quad$ (b) April $\quad$ (c) September (d) July (e) December

Key Concepts

Interpreting Mathematical Models in Context

Interpreting mathematical models means understanding the relationship between the variables in the equation and the real-world phenomena they represent. In this problem, the variable representing time (in months) must be aligned with the corresponding temperature values produced by the cosine-based model, providing meaningful predictions about temperature changes throughout the year.

Function Evaluation

Function evaluation involves substituting specific input values into a function in order to obtain corresponding output values. This concept is crucial for applying a mathematical model to real-life scenarios, allowing one to determine the temperature for specific months by plugging in the appropriate time values.

Trigonometric Functions

Trigonometric functions like cosine are used to represent periodic phenomena. The cosine function, with its well-known properties such as amplitude, period, and phase, offers a compact way to describe fluctuations, making it a powerful tool in modeling oscillatory behavior such as temperature variations.

Periodic Functions

Periodic functions repeat their values at regular intervals and are essential in modeling cyclical behavior observed in natural processes, such as seasonal temperature changes. They help in understanding patterns and predicting future values based on the cycle.

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