This course is designed to develop an understanding of topics which are fundamental to the study of Calculus. Emphasis is placed on the fundamentals of trigonometry and building an understanding of key concepts and techniques so you can progress to more challenging topics.
Yu will be provided with a student workbook which supplements the video lessons. You will have access to regular check of understanding with worked solutions.
You will start with the must know fundamentals by studying:
· Triangles
· Pythagoras Theorem
· Trigonometry Introduction
· Sine rule
· Worded problems using the sine rule
· The cosine rule – Calculating side length and angles
· Measuring angles
· Measuring angles in radians and Converting radians to degrees.
· Two special triangles
·
You will then build upon this base knowledge by studying:
· The unit circle
· Sine, cosine and tangent of angles in any quadrant with extra examples
· Graphs of sine and cosine trig functions
· Phase shift
· Changing amplitude and period of sine and cosine functions
· Vertical shift and putting it all the transformations together
How to get the most out of this course
This course is broken up into small individual sections designed to help you learn exactly what you need to know. The expertly crafted learning videos are designed to maximize your time. View the tutorial video and follow along. Pause and take notes as needed. After each of the tutorial videos you will find a ‘check of understanding’ which consists of 5 questions that relate to the material covered in the video/s. Complete the questions and check your Answers with the worked solutions so you can see how you are progressing.
Happy learning!
Kerry and Matt
Trigonometry – The must know fundamentals
Unit Circle, Periodic Functions, and transformations of functions.
-
2Triangles
Understand the key features of triangles.
-
3Pythagoras Theorem
Calculate the side lengths of right-angled triangles.
-
4Trigonometry Introduction
Understand the concept of the sine, cosine and tangent ratio for right angle triangles.
-
5Sine rule
Use the sine rule to calculate side lengths and angles of non-right angled triangles.
-
6Worded problems using the sine rule
Solving worded problems using the sine rule to calculate side lengths and angles of non-right angled triangles.
-
7The cosine rule - Calculating side length and angles
Calculate the side length and angles of non-right angled triangles using the cosine rule
-
8The cosine rule- Calculating angle
Calculate the side length and angles of non-right angled triangles using the cosine rule
-
9Measuring angles
Convert between degrees, minutes and seconds (DMS).
-
10Measuring angles in radians
Represent angle measure in radians.
-
11Converting radians to degrees
Convert between degrees and radians
-
12Two special triangles
Use special triangles to represent sine, cosine and tangent of common angles (30, 45, 60) in both degrees and radians.
(Additional Lessons) – Solving Trigonometric equations
-
13The unit circle
Use the unit circle to calculate the sine, cosine and tangent of angles that are not acute.
-
14Sine, cosine and tangent of angles in any quadrant (Part 1)
Understand how the unit circle can be used to calculate sine, cosine and tangent of angles that are in any quadrant
-
15Sine, cosine and tangent of angles in any quadrant (Part 2)
A variety of examples to help understand how the unit circle can be used to calculate sine, cosine and tangent of angles that are in any quadrant
-
16Graphs of sine and cosine trig functions
Relate the unit circle to the graphs of sine and cosine.
-
17Phase shift
Perform horizontal transformation of sine and cosine functions.
-
18Changing amplitude and period of sine and cosine functions
Change the period and amplitude of sine and cosine functions.
-
19Vertical shift and putting it all the transformations together (Part 1)
Perform vertical, horizontal phase shifts, changes in amplitude and period changes to sine and cosine functions.
-
20Vertical shift and putting it all the transformations together (Part 2)
Worked example consisting of a variety of transformations.