You use the cosine rule when you either

-know the lengths of all sides [to find any angle],

-know one angle, and the lengths of the sides meeting at that angle [so you can find the length of the side opposite the angle]

You can use the sine rule if you know an angle and the length of a side opposite, and either one other side or angle:

Say you know A, B, and b

then a = bsinA/sinB

Say you know a, B and b

sinA = asinB/b

Basically, use them whenever you know some stuff about a triangle, and need to find another side length, or another angle.

Could I ask someone to correctly expand Rcos(x+a) for me please?

I have the cos(a+b) = cosAcosB - sinAsinB

which would mean that Rcos(x+a) = Rcos(x)cos(a) - Rsin(x)sin(a)

However, in my notes it has Rcos(x)cos(a) + Rsin(x)sin(a)

If someone could clear up this minor query it would help a lot!

Thanks

w00tt

Your notes are wrong. It has a minus sign.

You need the chain rule to differentiate 4sin(2y+6) (with respect to y)

So, let R = 2y + 6

and z = 4sinR

=>dR/dy = 2

dz/dR = 4cosR

=>dz/dy = 2*4cos(2y+6)

=8cos(2y+6)

So yes, you do need to differentiate the 2y+6 bit as part of the chain rule

Assuming PV means previous values, you have (in degrees):

sin: pv + 360n, 180 - pv

cos: pv + 360n, -pv

tan: pv + 180n

There are probably more.

Would somebody be willing to quickly explain arcsin/arccos/arctan to me? I know that they are sin^-1, cos^-1 tan^-1, but what do I do with them?

Using the derivative of sin x and cos x show that d(tanx)/dx= sec^2x?

So using sin and cos identities to get the RHS then differentiating once you get to tan??

Any help will be appreciated.

w00tt

Could someone show the working out on how to answer this question.

An alloy is formed between 3 metals (A, B and C) and weighs a total of 550g.

There is twice as much of A than B and one and a half times as much of B than C.

How much of the metal M is in the alloy?

Express your final answer as a % of the total weight of the alloy.

As jpowell I do not really get the question...

but possibly I could interpret it as 1.5*2A+1.5B+1C=550

And assuming the metals A, B and C have the same relative molecular mass (which they won't have in reality) you can easily solve it. (or well, this depends on what you mean by 'much' if it refers to by mass or by number of particles, if mass there will be no problem of assuming anything...the question is not clear...)

But, IF the above is correct I guess it is just 6/11 of A 3/11 of B and 2/11 of C

I mean A lol!

Thanks Nota, your correct

Can anyone help me with the following question? I keep ending up with an answer that's different from the answer in the back of the book, so I want to check I'm actually doing something wrong.

The question's:

Find the gradient for this curve {xlny^3=6} at (2,e):

I keep ending up with the answer: {-e^3}/4 however the answer in the back is -e/2

Can anyone help me please?!

lny = 2/x

y = e^(2/x)

dy/dx = -(2e^(2/x))/x^2

dy/dx at x = 2 is -e/2

Thanks a lot for the answer. Rep is on it's way!

Hint: [x^(1/4)]^4 = x^(1/4 * 4) = x^1 = x