Grades 9/10/11 Exponential and Trigonometric Functions

Exponential and sinusoidal functions. Properties, transformations, and applications.

This is one of seven strands of the CEMC Grade 9/10/11 courseware. The other strands and more information about this courseware is available on the Grade 9/10/11 homepage

Unit 1: Exponential Functions

In this lesson, we introduce the exponential function and use it to describe a variety of applications involving exponential growth and exponential decay.

In this lesson, we discuss the domain, range, intercepts, and asymptotes of a basic exponential function.

In this lesson, we determine the equation of an exponential function describing a given table of values or graph. We also show how to use finite differences to identify data sets that are representative of exponential processes.

In this lesson, we find an equation to describe an exponential function that has undergone reflection, stretch, and translation transformations. We also look at how to graph transformed exponential curves.

In this lesson, we see that a given exponential function can be written in different bases.

In this lesson, we look at how to develop mathematical models to describe exponential processes using transformed exponential functions.

All of the pencil and paper practice exercises, answers, and solutions for this unit are reproduced here.

This is a collection of additional, and sometimes challenging, problems that extend the material covered in this unit, connect material from different lessons, and further explore real-world applications.

Unit 2: Sinusoidal Functions

Periodic phenomena appear in many different settings. In this lesson, we will learn to recognize and describe periodic behaviour mathematically. 

The sine and cosine ratios depend on the input angle so these operations can be expressed as functions. In this lesson, we introduce the functions ‌\(y=\sin(x^\circ)\) and ‌\(y=\cos(x^\circ)\) and identify their key properties.

This lesson explores the effects of vertical and horizontal reflections, stretches, and translations on the properties of sinusoidal functions. We will use these properties to help us graph simple transformations of \(f\left(x\right)=\sin\left(x^\circ\right)\) and \(f\left(x\right)=\cos\left(x^\circ\right)\).

In this lesson, we will combine transformations to graph sinusoidal functions. We will learn to identify the properties of these functions from their equations \(y = a\sin\left(b\left(x -h\right)^\circ\right) + k\) and \(y = a\cos\left(b\left(x -h\right)^\circ\right) + k\).

In this lesson, we relate real-world periodic behaviour to the properties of sinusoidal functions. We will determine equations to model the graphs of sinusoidal functions and real-world phenomena. 

This lesson examines real-world situations that relate to sinusoidal behaviour or where data can modelled by sinusoidal functions.

All of the pencil and paper practice exercises, answers, and solutions for this unit are reproduced here.

This is a collection of additional, and sometimes challenging, problems that extend the material covered in this unit, connect material from different lessons, and further explore real-world applications.