Trigonometric graphs (Radians and degrees)
Keywords
| Standard trigonometric curves | 標準的な三角関数の曲線 | 표준 삼각함수 곡선 | 标准三角函数曲线 |
| Graph transformations | グラフの変換 | 그래프 변형 | 图形变换 |
| Amplitude | 振幅 | 진폭 | 振幅 |
| Period | 周期 | 주기 | 周期 |
| Translate | 平行移動 | 변환하다 | 平移 |
| Reflect | 反射 | 반사하다 | 反射 |
| Scale | スケール変更 | 확대/축소하다 | 缩放 |
Inquiry questions
Factual Inquiry Questions
What are standard trigonometric curves?
How are they mathematically defined?
Can you provide examples of standard trigonometric curves?
What are the key characteristics of these curves?
Conceptual Inquiry Questions:
How does recognizing and finding equations for transformed curves relate to function composition?
How do translation, reflection, and scaling apply to transforming trigonometric curves?
What are real-world applications or contexts where transformed trigonometric curves are relevant?
Debatable Inquiry Questions:
How do graph transformations affect trigonometric curves?
How do transformations alter amplitude and period?
Can a transformed trigonometric curve lose its periodicity?
What is the significance of recognizing and applying graph transformations to trigonometric curves?
Objectives:
Know and recognise standard trigonometric curves.
Apply graph transformations to them.
Recognise and find equations for transformed curves.
Initial look at where trigonometric curves come from.
Some background around how the circle relates to trigonometry. We will look at this in considerably more depth in Part 2 of trigonometry. For part 1 test we will work upto and including transforming trigonometric curves.
The original trigonometric functions are the starting point. Knowing the basic shapes is very useful. Here are the important values in degrees. Sometimes we will work with the graphs in radians too.
These graph transformations are the same for all functions. You can refresh your memory with the applet below.
Can you predict what the transformed curves will look like?
Useful vocabulary when describing features of trigonometric curves
Supplementary video
Check out this video if you are unsure about how the curve is transformed
Trigonometric graph transformations
Find the equations of these curves without graphics calculator.
Check with graphics calculator to test your answer,
Trigonometric functions - Exam style questions
Practice questions
Question 1-12
Exam style - Section A - Short response
Question 13-33
Exam style - Section B - Long response
Question 34-39, 42-43
Extension Question 40,41 - Challenging
![[MAA 3.7] TRIGONOMETRIC FUNCTIONS.pdf](https://stage.geogebra.org/resource/yyv7trbw/4uGY1yNvFYkWjU5k/material-yyv7trbw-thumb.png)
![[MAA 3.7] TRIGONOMETRIC FUNCTIONS_solutions.pdf](https://stage.geogebra.org/resource/ptssddkd/nIjvW99AXVuCXSWb/material-ptssddkd-thumb.png)