Selected: Edexcel A Level Maths - Pure Maths
AS & A2 (Whole Course) - Casio fx-991EX
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AS & A2 (Whole Course) - Casio fx-991EX
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OCR (A) H230/02 Jun 2023 AS Exam Q. 3 : 8 marks in 9:36 min.
OCR (A) H240/03 Nov 2021 A2 Exam Q. 5 : 6 marks in 7:12 min.
OCR (A) H240/01 Jun 2019 A2 Exam Q. 9 : 11 marks in 13:12 min.
Edexcel 9MA0/01 Jun 2023 A2 Exam Q. 13 : 7 marks in 8:24 min.
Edexcel 9MA0/02 Jan 2023 A2 Mock Q. 13 : 8 marks in 9:36 min.
Edexcel 8MA0/01 Jun 2022 AS Mock Q. 16 : 10 marks in 12:00 min.
Edexcel 9MA0/02 Jun 2022 A2 Exam Q. 9 : 5 marks in 6:00 min.
Edexcel 9MA0/02 Dec 2021 A2 Mock Q. 8 : 9 marks in 10:48 min.
Edexcel 9MA0/02 Nov 2021 A2 Exam Q. 15 : 11 marks in 13:12 min.
Edexcel 9MA0/01 Oct 2020 A2 Exam Q. 6 : 7 marks in 8:24 min.
Edexcel 9MA0/02 Mar 2020 A2 Mock Q. 10 : 9 marks in 10:48 min.
Edexcel 9MA0/01 Jan 2019 A2 Mock Q. 7 : 8 marks in 9:36 min.
Edexcel 9MA0/01 Jun 2018 A2 Exam Q. 8 : 5 marks in 6:00 min.
Edexcel 9MA0/01 May 2018 A2 Mock Q. 13 : 11 marks in 13:12 min.
Edexcel 9MA0/02 May 2017 A2 Sample Exam Q. 13 : 9 marks in 10:48 min.
Explore transforming trigonometric graphs for modelling
Explore maxima and minima of trigonometric curves
Trig Applications: Page 189, Example 21
Visualise a sin x ${ \pm }$ b cos x to sin
This display allows you to visualise the transformations:
$\color{purple}{ a \, \sin (x) + b \, \cos (x) = R \, \sin (x + \alpha) }$
$\color{purple}{ a \, \sin (x) - b \, \cos (x) = R \, \sin (x - \alpha) }$
After adjusting $\color{red}{a}$ and $\color{blue}{b}$, you can adjust $\color{green}{r}$ and $\color{green}{\alpha}$ to their derived values to see the two curves coincide.
For a better view, you should use the navigation buttons in the lower right corner to zoom in and out.
$\color{purple}{ a \, \sin (x) + b \, \cos (x) = R \, \sin (x + \alpha) }$
$\color{purple}{ a \, \sin (x) - b \, \cos (x) = R \, \sin (x - \alpha) }$
After adjusting $\color{red}{a}$ and $\color{blue}{b}$, you can adjust $\color{green}{r}$ and $\color{green}{\alpha}$ to their derived values to see the two curves coincide.
For a better view, you should use the navigation buttons in the lower right corner to zoom in and out.
Visualise a cos x ${ \pm }$ b sin x to cos
This display allows you to visualise the transformations:
$\color{purple}{ a \, \cos (x) + b \, \sin (x) = R \, \cos (x - \alpha) }$
$\color{purple}{ a \, \cos (x) - b \, \sin (x) = R \, \cos (x + \alpha) }$
After adjusting $\color{red}{a}$ and $\color{blue}{b}$, you can adjust $\color{green}{r}$ and $\color{green}{\alpha}$ to their derived values to see the two curves coincide.
For a better view, you should use the navigation buttons in the lower right corner to zoom in and out.
$\color{purple}{ a \, \cos (x) + b \, \sin (x) = R \, \cos (x - \alpha) }$
$\color{purple}{ a \, \cos (x) - b \, \sin (x) = R \, \cos (x + \alpha) }$
After adjusting $\color{red}{a}$ and $\color{blue}{b}$, you can adjust $\color{green}{r}$ and $\color{green}{\alpha}$ to their derived values to see the two curves coincide.
For a better view, you should use the navigation buttons in the lower right corner to zoom in and out.