In this recording use the inverse function rule for differentiation to find the derivate of the inverse sine of x. This example includes discussion of the importance of looking at the graph of such a function, to see whether it is increasing or

Why are circles, ellipses, parabolas and hyperbolas called 'conic sections'? Part 1 (MathsCasts)

Jan 17th, 2014 10m 16s

We solve simultaneously the equations of a plane and a cone and show that the intersections are circles, parabolas, ellipses, hyperbolas, straight lines or just the origin.

Why is the graph of y = 1/x an hyperbola? (MathsCasts)

Sep 26th, 2013 12m 19s

We demonstrate that the equation y = 1/x transforms to standard form for an hyperbola under rotation of the coordinate axes by 45 degrees.

Simplifying compositions of trig and inverse trig functions (MathsCasts)

Sep 23rd, 2013 5m 52s

Two examples of simplifying expressions of the form trig(inverse trig), using right angled triangles. The result is in algebraic form without trig functions

Properties of sin and cos - Part 2 (MathsCasts)

Sep 5th, 2013 9m 51s

We prove some results on horizontal shifts applied to the sin and cos functions.

Properties of sin and cos - Part 1 (MathsCasts)

Sep 5th, 2013 8m 26s

We prove that cos(-x) = cos(x) and sin(-x) = - sin(x|)

A Geometric proof of the sum and difference formulae for sin and cos (MathsCasts)

Aug 27th, 2013 11m 47s

We prove the formula for sin(A-B) using right-angled triangles then we show how the corresponding formulae for cos(A-B) and sin and cos of A+B can be deduced as a result.

Compass directions: Part 2 (MathsCasts)

Jan 30th, 2013 8m 6s

We look at a second example involving combinations of direction, one of which is none of north, south, east or west.

Compass directions: Part 1 (MathsCasts)

Jan 23rd, 2013 10m 9s

We introduce the points of the compass and solve a simple example using distances and basic directions (N,S,E,W) to find resulting distance and angle.

Writing composite trigonometric functions as algebraic expressions (MathsCasts)

Oct 19th, 2012 14m 2s

Several examples are given of rewriting composite circular functions, where the inner function is an inverse trigonometric function, as an algebraic function in terms of x.

Parallel planes (MathsCasts)

Apr 27th, 2012 4m 2s

Explains how the equations of two parallel planes are related - then solves a problem where a plane parallel to a given plane, passing through a point, is to be found.

Complex regions (MathsCasts)

Mar 21st, 2012 6m 32s

This recording looks at how to identify the nature of the region in the complex plane that satisfies |z-z0|=r. This is then illustrated further with a specific example.

Sketching polar curves (MathsCasts)

Feb 7th, 2012 9m 56s

An explanation is given of the general visual interpretation of polar coordinates. An example of then given of choosing different angles, evaluating 'r' at each of these angles and then plotting and joining the resulting points by hand.

Polar and cartesian curves (MathsCasts)

Dec 8th, 2011 5m 58s

This recording explains the relationship between Polar and Cartesian coordinates of a 2D curve. An example is then given of converting a polar equation into Cartesian form and an example is given of converting a Cartesian equation into polar fo

Intersection of a line and a plane (MathsCasts)

Dec 6th, 2011 5m 32s

Considering a line written in scalar parametric form and a plane written in form ax + by + cz = d, three examples investigate if and where line and plane intersect: in one point; the line lies on the plane; or line and plane are parallel and ne

Equation of a plane given its normal and a point on it (MathsCasts)

Dec 5th, 2011 2m 37s

This recording starts by showing how the equation of a plane relates to its normal vector. An example is then done to show how this allows us to find the equation of a plane, provided we also know a point on the plane.

Equation of a plane given a point and a line on the plane (MathsCasts)

Dec 2nd, 2011 7m 6s

Given a point and a line on a plane, we find the equation of the plane.A second point on the plane is identified, and hence a vector on the plane. A normal vector to the plane is calculated using the vector product.The equation of the plane is

Converting a parametric curve to Cartesian form (MathsCasts)

Nov 29th, 2011 4m 16s

This screencast gives two examples of converting the parametric equations of 2D curves into Cartesian equations, and includes a discussion on the importance of considering any restrictions of the domain of the resulting Cartesian equations in e

Angle between two planes (MathsCasts)

Nov 28th, 2011 4m 24s

This recording starts by giving the general formula for calculating the angle between two planes by finding the angle between their normal vectors. An example is then given to illustrate this.

Sketching 3D Surfaces: Example 1 (MathsCasts)

Sep 8th, 2011 10m 14s

This screencast gives an example of sketching vertical and horizontal cross-sections of a surface and hence producing a final sketch of the resulting 3D surface (which is an elliptical hyperboloid of two sheets)

Angle between a line and a plane (MathsCasts)

Aug 29th, 2011 5m 34s

Example where equation of a plane and scalar parametric equations of a line are given. To find the angle between the line and the plane, the equations of the line are converted to vector form, the angle between the line and the normal vector to

Directional derivatives (MathsCasts)

Aug 29th, 2011 6m 4s

An example where the gradient of a surface is found depending on the angle alpha, and then the maximum gradient is calculated.

Equation of a plane given three points (MathsCasts)

Aug 19th, 2011 4m 57s

Application of vectors to the example of finding the equation of a plane through three points by first determining two vectors on the plane, then using the cross product to determine a normal vector to the plane, then using the normal vector an

Non right-angled triangles (MathsCasts)

Aug 10th, 2011 4m 50s

This screencast gives explanation of two rules for finding unknown angles and/ or lengths of sides in any triangle: the Sine Rule and the Cosine Rule. Examples are then given to show how to apply each rule in practice.

Right-angled triangles (MathsCasts)

Aug 10th, 2011 3m 58s

The screencast begins by outlining the rules for finding angles in a right-angled triangle given the lengths of two of its sides. Examples are then given of applying these rules: both to finding an angle given the length of two sides in a right