Further Maths

Differentiating ln(1+sinx) up to and including the term x³.

Maclaurin for sinx up to x³ term. Sub into Maclaurin for ln(1+x).

How to work out the inverse of a 3×3 matrix?

First work out the determinant. Then work out the cofactor matrix. Then transpose the cofactor matrix. Then multiply that by 1 over the determinant.

What is Σr?

n/2(n+1)

How to find the angle between two planes?

Use cosθ equation.

How to find the angle between a line and a plane?

Use cosθ equation then takeaway answer from 90.

How to work out the cartesian equation of a plane from the vector equation of a plane?

Use the cross product of the direction vectors to get your normal then sub in your general point to get d.

What is cosθ in exponential form?

cosθ=1/2(e^θi + e^-θi)

What is sinθ in exponential from?

sinθ=1/2i(e^θi - e^-θi)

What is the formula for a volume of revolution around the x-axis?