Question

because the values of circular functions repeat every 2π, they are used to describe things that repeat periodically. for example, the maximum afternoon temperature in a given city might be modeled by the formula below. in the formula, t represents the maximum afternoon temperature in month x, with x = 0 representing january, x = 1 representing february, and so on. t = 55 - 30 cos(xπ/6) the maximum afternoon temperature in february is 25° (round to the nearest integer as needed)

Explanation:

Step1: Identify the value of x for February

Since x = 1 represents February, we substitute x = 1 into the formula $t = 55-30\cos\frac{x\pi}{6}$.

Step2: Calculate the cosine - value

Substitute x = 1 into $\cos\frac{x\pi}{6}$, we get $\cos\frac{\pi}{6}=\frac{\sqrt{3}}{2}\approx0.866$.

Step3: Calculate the temperature t

$t = 55-30\times0.866=55 - 25.98 = 29.02\approx29$.

Answer:

29