##### Edexcel 9MA0/01 Jun 2022 A2 Exam Q. 14 : 8 marks in 9:36 min.

##### Edexcel 9MA0/01 Nov 2021 A2 Exam Q. 10 : 8 marks in 9:36 min.

##### Edexcel 9MA0/02 Oct 2020 A2 Exam Q. 10 a : 4 marks in 4:48 min.

##### Edexcel 9MA0/01 Mar 2020 A2 Mock Q. 6 : 6 marks in 7:12 min.

##### Edexcel 9MA0/01 Mar 2020 A2 Mock Q. 8 bc : 6 marks in 7:12 min.

##### Edexcel 9MA0/02 Jun 2019 A2 Exam Q. 12 a : 4 marks in 4:48 min.

##### Edexcel 9MA0/02 Jun 2019 A2 Shadow Exam Q. 12 a : 4 marks in 4:48 min.

##### Edexcel 9MA0/02 Jun 2018 A2 Exam Q. 12 a : 3 marks in 3:36 min.

##### Edexcel 9MA0/02 May 2018 A2 Mock Q. 13 : 10 marks in 12:00 min.

##### Prove addition formulae using geometric construction

##### Visualise sin(2x) Double Angle Formulae

Initially, $\color{green}{a}$ is set to 0 so you can visualise how $\color{red}{\sin (c \, x) \cos (c \, x)}$ arises as the product of $\color{grey}{\sin (c \, x)}$ and $\color{grey}{\cos (c \, x)}$.

Then, by adjusting $\color{green}{a}$, $\color{red}{b}$ and $\color{red}{c}$ to make the green and red curves coincide, you can view the double angle formulae, not only for $\color{green}{\sin (2 \, x)}$, but for other values of $\color{green}{a}$ too.

##### Visualise cos(2x) Double Angle Formulae

By adjusting $\color{green}{a}$, $\color{red}{b}$, $\color{red}{c}$ and $\color{red}{d}$ to make the green and red curves coincide, you can view the double angle formulae, for $\color{green}{\cos (2 \, x)}$ in its different forms.

##### Visualise sin(x ${ \pm }$ a) Addition Formulae

$\color{purple}{ \sin (x + a) = \sin(x) \cos(a) + \cos(x) \sin(a) }$

$\color{purple}{ \sin (x - a) = \sin(x) \cos(a) - \cos(x) \sin(a) }$

##### Visualise cos(x ${ \pm }$ a) Addition Formulae

$\color{purple}{ \cos (x + a) = \cos(x) \cos(a) - \sin(x) \sin(a) }$

$\color{purple}{ \cos (x - a) = \cos(x) \cos(a) + \sin(x) \sin(a) }$

##### Visualise a sin x ${ \pm }$ b cos x to sin

$\color{purple}{ a \, \sin (x) + b \, \cos (x) = R \, \sin (x + \alpha) }$

$\color{purple}{ a \, \sin (x) - b \, \cos (x) = R \, \sin (x - \alpha) }$

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

$\color{purple}{ a \, \cos (x) + b \, \sin (x) = R \, \cos (x - \alpha) }$

$\color{purple}{ a \, \cos (x) - b \, \sin (x) = R \, \cos (x + \alpha) }$

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.