The Unit Circle

The unit circle is a circle of radius 1 that we can use to pull together Pythagoras and trigonometry. The unit circle has the equation: (1) This looks like this: If we project a line from the origin to a point on the unit circle we get: If we construct a triangle from this […]

Angles

Angles are used to measure the separation between two objects or lines. There are 2 common ways of expressing an angle. The first is degrees, there are 360º in a full circle, so quarter of a circle is 90º, and an eighth of a circle is 45º. It is convention to measure angles in an […]

Pythagoras and Trigonometry

Triangles are a 3 sided polygon, whose internal angles all add up to 180°. A triangle with one angle of 90° is called a right angle triangle. An example is: If we are looking to find the lengths of the sides of the right angle triangle, and we know the lengths of any 2 of […]

Factoring Quadratics

If we have a quadratic of the form it can be useful to put it in the form , as this will give us two equations that will give us both of the solutions of the quadratic, one is and the other is . So first if we are given the factored form of the […]

Completing the Square

Another method of solving a quadratic is to complete the square. This changes the form of the quadratic from (1) Into the form (2) We can use the square of a binomial: (3) Using this we can see that for any equation of the form , in other words, where we can […]

Ellipses

Firstly an ellipse is a squashed circle, and a circle is just a special type of ellipse. The general formula for an ellipse is: (1) Where is the radius of the ellipse, is the radius of the ellipse in the x-direction and b is the radius of the ellipse in the y-direction. Therefore a […]

Quadratics

A quick intro to quadratics! First a quadratic is any equation of the form where a,b & c are any real numbers, they produces a graph of the shape: Solving a quadratic, means we are finding the locations where the function equals zero, which is where the function crosses the y-axis, when . These locations […]