Module 6 Summary

In this module you investigated the following question: How can a sinusoidal function be used to model and solve cyclical problems?

 

You explored sinusoidal functions. The first thing you learned about was the radian, which is an angular measure. Next, you explored some angles that were larger than 360°. You were then introduced to the sine and cosine functions and interpreted various other sinusoidal functions. You then used the parameters a, b, c, and d to describe characteristics of a sinusoidal function from an equation. Finally, you used curves of best fit and regression equations to help interpret sinusoidal data.

 

In the Module 6 Project: Applications of Sinusoidal Functions, you explored how latitude and the time of year affected the number of hours of daylight. You then modelled hours of daylight data using a sinusoidal curve.

 

Following are some of the key ideas you learned in each lesson.

 

Lesson 1	A radian is the size of angle produced at the centre of a circle by a radius laid along the circumference of the circle.     Angles larger than 360° are often represented with a spiral.
Lesson 2	The maximum, minimum, midline, amplitude, and period are characteristics commonly used to describe a sinusoidal function.
Lesson 3	Characteristics of the functions y = a sin b(x – c) + d and y = a cos b(x – c) + d can be found by interpreting each parameter separately.
Lesson 4	Data that follows a sinusoidal pattern can be modelled using a curve of best fit or a regression equation.