Trigonometric Functions and Day Length

The video tutorial explains how to model the length of daylight in Juneau, Alaska, using a trigonometric function. It starts by discussing the longest and shortest days of the year and introduces the concept of using a trigonometric function to model day length. The tutorial uses an intermediary variable, U, to simplify the process and calculates the amplitude, midline, and period of the function. Finally, it substitutes U with T to express the function in terms of the day of the year, providing a complete model for the length of daylight throughout the year.

What is the longest day of the year in Juneau, Alaska?

• September 21st

• March 21st

• December 21st

• June 21st

How many days after June 21st is represented by the variable U?

• 172 days

• 0 days

• 365 days

• 182 days

What is the relationship between U and T?

• U = 172 - T

• U = T

• U = T + 172

• U = T - 172

Which trigonometric function is used to model the day length?

• Tangent

• Cosine

• Sine

• Secant

What is the maximum value of the cosine function in this model?

• 1

• 357

• 0

• 739.5

What is the midline value of the trigonometric function?

• 382.5

• 357

• 1,096.5

• 739.5

How is the amplitude of the function calculated?

• By multiplying the midline by two

• By dividing the maximum value by two

• By subtracting the midline from the maximum value

• By adding the maximum and minimum values

What is the period of the trigonometric function in terms of days?

• 365 days

• 182.5 days

• 730 days

• 90 days

What is the value of B in the function?

• 2π

• π/365

• 2π/365

• 365/2π

What is the final expression for L(T)?

• L(T) = 739.5 * cos(2π/365 * (T - 172)) + 357

• L(T) = 357 * cos(2π/365 * (T - 172)) + 739.5

• L(T) = 357 * sin(2π/365 * (T - 172)) + 739.5

• L(T) = 739.5 * sin(2π/365 * (T - 172)) + 357