Search our library of Further Mathematics questions

Top answers

Further Mathematics

All levels

Lengths of two sides of the triangle and the angle between them are known. Find the length of the third side and the area of the triangle.

We don't know what type of a triangle we're considering here. Therefore the universal and quickest solution to the first problem is use of the cosine rule, which states that for a triangle with sides a,b ...

Answered by Szymon K. • Further Mathematics tutor

6696 Views

write 2-2i in its modulus argument form

firsly sketch out the 2-2i on an argand diagrm and draw a line from (0,0) to (2,-2). With the shortest distance Mark the angle theta from the positive x-axis to the line to see whether the argument is ...

Answered by Zivanayi S. • Further Mathematics tutor

8489 Views

Find the inverse of the general 2x2 matrix A= ([a, b],[c, d]) when does this inverse exist?

This is a typical further maths question, doing it correctly is a matter of carrying out a two-step process.

Start by finding the determinant of the matrix,

det(A)=ad-bc

Answered by Larry R. • Further Mathematics tutor

2935 Views

The curve C has polar equation 'r = 3a(1 + cos(x)). The tangent to C at point A is parallel to the initial line. Find the co-ordinates of A. 0<x<pi

Tangent is parallel, therefore (dy/dx)=0.

Find y:

y = r sin(x) = 3a(1 + cos(x))(sin(x))

Differentiate y with respect to x

dy/dx = 3a[(2cos(x) - 1...

Answered by Salah S. • Further Mathematics tutor

6432 Views

Given that f(x)=2sinhx+3coshx, solve the equation f(x)=5 giving your answers exactly.

Firstly set 2sinhx+3coshx=5Now using the exponential definitions of sinhx and coshx rewrite the equation to give:2(1/2(e^x-e^-x))+3(1/2(e^x+e^-x))=5Simplify the equation by expanding out the brackets, mul...

Answered by Emily-Louisa S. • Further Mathematics tutor

7033 Views