The Edexcel C3 (14/06/12 - AM) Revision Thread

Multiplication first then addition. BODMAS

Jan 09

^^ doesnt matter, if you shift it right by 1 first or horizontal stretch of 1/2 first, you get the same thing, try it

Ugh, can't be bothered to do any more papers. I think I'm just going to revise the inverse graph for cot. It's the only thing I don't understand.

Can someone please check these? The first few are obvious, but the last couple I'm not sure about:

$f(-x)$ is a reflection in the y-axis.
$-f(x)$ is a reflection in the x-axis.
$f(ax)$ is a stretch scale factor 1/a in the x direction.
$af(x)$ is a stretch scale factors a in the y-direction.
$|f(x)|$ is reflecting only the quadrants where y is negative into the positive y quadrants (and leave the rest of the function).
$f(|x|)$ is mirroring all x>0 into the negative x quadrants.
$f(-|x|)$ is mirroring all values where x<0 into the positive x quadrant.
$-|f(x)|$ is just like |f(x)| but then you reflect it in the x-axis.
$f(1/x)$ is... I don't know but I've never seen it come up!

Correcto? And any important ones I missed?

Lol , dw, I'm a quick typer.

Erm, ok so 8aii

We know that y = arccos

So that must mean that cos(y) = x

Sin graphs and cos graphs are really similar, they are only pi/2 out of phase, or a translation to the right (by pi/2)

That means that we know

sin(x) = cos(x-pi/2)
or
cos(x) = sin(pi/2 - x)

In this case you can sub in the values so

x = sin(pi/2 - y)

That should be your answer.

As for the second part, you know what arcsin and arccos are, sub in and you'll get:

y + (pi/2 -y)

as in the tan graph?

Can someone please check these? The first few are obvious, but the last couple I'm not sure about:

$f(-x)$ is a reflection in the y-axis.
$-f(x)$ is a reflection in the x-axis.
$f(ax)$ is a stretch scale factor 1/a in the x direction.
$af(x)$ is a stretch scale factors a in the y-direction.
$|f(x)|$ is reflecting only the quadrants where y is negative into the positive y quadrants (and leave the rest of the function).
$f(|x|)$ is mirroring all x>0 into the negative x quadrants.
$f(-|x|)$ is mirroring all values where x<0 into the positive x quadrant.
$-|f(x)|$ is just like |f(x)| but then you reflect it in the x-axis.
$f(1/x)$ is... I don't know but I've never seen it come up!

Correcto? And any important ones I missed?

the ones bolded should be the opposite, so where it says x-axis it should be y and vice versa

AQA you say?

That would be the reciprocal graph of cot:
If his/her wording is correct, they mean arccot.

Do we need to know cot, sec, cosec, arctan etc graphs?

Does that include if its something like Af(x-1)?

isn't arccot tan as well??

Lol , dw, I'm a quick typer.

Erm, ok so 8aii

We know that y = arccos

So that must mean that cos(y) = x

Sin graphs and cos graphs are really similar, they are only pi/2 out of phase, or a translation to the right (by pi/2)

That means that we know

sin(x) = cos(x-pi/2)
or
cos(x) = sin(pi/2 - x)

In this case you can sub in the values so

x = sin(pi/2 - y)

That should be your answer.

As for the second part, you know what arcsin and arccos are, sub in and you'll get:

y + (pi/2 -y)

Do we need to know cot, sec, cosec, arctan etc graphs?