the number of hours of daylight on a given day in city a is given by the following function, where x is the…

the number of hours of daylight on a given day in city a is given by the following function, where x is the number of days after january 1. y = 2 sin((2π/365)(x - 80))+12. use this function to answer parts a through e. a. what is the amplitude of this function? 2 (simplify your answer.) b. what is the period of this function? (simplify your answer. type an exact answer, using π as needed. use integers or fractions for any numbers in the expression.)

the number of hours of daylight on a given day in city a is given by the following function, where x is the number of days after january 1. y = 2 sin((2π/365)(x - 80))+12. use this function to answer parts a through e. a. what is the amplitude of this function? 2 (simplify your answer.) b. what is the period of this function? (simplify your answer. type an exact answer, using π as needed. use integers or fractions for any numbers in the expression.)

Answer

Explanation:

Step1: Recall amplitude - formula

For a sine function of the form $y = A\sin(B(x - C))+D$, the amplitude is given by $|A|$. In the function $y = 2\sin\left(\frac{2\pi}{365}(x - 80)\right)+12$, $A = 2$. So the amplitude is 2.

Step2: Recall period - formula

For a sine function $y = A\sin(B(x - C))+D$, the period is given by $T=\frac{2\pi}{|B|}$. Here, $B=\frac{2\pi}{365}$. So, $T=\frac{2\pi}{\frac{2\pi}{365}}$.

Step3: Calculate the period

When we divide $2\pi$ by $\frac{2\pi}{365}$, we get $T = 365$.

Answer:

a. 2 b. 365