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Mathematics

Understanding Supplementary and Complementary Angles

Supplementary and complementary angles are useful concepts to understand in trigonometry. Supplementary angles are any two angles that sum (add) up to 180° (a straight line). An easy way to remember this is that Supplementary and Straight line both begin with the letter ‘S’. Complementary angles are any two angles that sum (add) up to […]

Mathematics

Proving the Law of Sines

A tutorial on the Law of Sines can be found here. Assumes an understanding of the trigonometric function sine. A basic tutorial can be found here and a tutorial using the Unit Circle can be found here. The Law of Sines says that “given any triangle (not just a right angle triangle): if you divide […]

Mathematics

Understanding the Law of Sines

While trigonometry is used to solve problems involving right angle triangles, it can also be applied to triangles that are not right angle triangles. Assumes you understand basic trigonometric concepts. A tutorial on understanding sine, cosine and tangent can be found here. A tutorial on understanding the trigonometric functions and the unit circle can be […]

Mathematics

Understanding Basic Trigonometric Identities

This tutorial assumes you are familiar with the trigonometric functions and their derivation from the unit circle. A tutorial on the trigonometric functions can be found here. A tutorial on the trigonometric functions and the unit circle can be found here. What is an Identity? An identity (in mathematics) is something that is true (more […]

Mathematics

How to Solve Trigonometric Problems

This tutorial offers advice on how to solve trigonometric problems and provides several problems worked through in detail. It assumes you are familiar with the trigonometric functions sine, cosine, tangent, secant, cosecant, and cotangent. A basic tutorial can be found here. A more advanced tutorial can be found here. If an explanation / walkthrough is […]

Mathematics

Understanding Trigonometric Functions using the Unit Circle (Advanced)

While I call this advanced, it does not mean harder or more complicated, it just means more abstract. Understanding the trigonometric functions (sine, cosine, tangent) using right angle triangles is simply a special case of trigonometric functions using the unit circle. I strongly recommend first reading and understanding the article Understanding Sine, Cosine, and Tangent […]

Mathematics

Understanding Sine, Cosine and Tangent

An article explaining trigonometric functions using the unit circle can be found here Using the unit circle is the standard way trigonometric functions are defined and understood in mathematics. I recommend reading and understanding this article first. Later, if you want to understand how trigonometric functions are defined for values greater than 90° or less […]

Mathematics

Understanding Averages – Mean, Median, and Mode

This tutorial examines the concept of the average as a single value representing a collection of values. It focusses on the mean, median, and mode. The average (especially in physics) can also mean the center or balance point, but, for most everyday use, we tend to think of the average as representative value. Average comes […]

Mathematics

Proving Alternate Interior Angles are Congruent (the same)

The Alternate Interior Angles Theorem states that If two parallel straight lines are intersected by a third straight line (transversal), then the angles inside (between) the parallel lines, on opposite sides of the transversal are congruent (identical). This is illustrated in the image below: We see two parallel lines and a third line (transversal) intersecting […]

Mathematics

Proving that the Angles in a Triangle Sum up to 180°

Proving that the angles inside a triangle – any triangle – sum up to 180° is very simple, but leaves most people unsatisfied (or unconvinced) because it depends on the properties of something called Alternate Interior Angles. I’ll give the proof first and then explain Alternate Interior Angles A demonstration of the angles of a […]

Mathematics

Demonstrating that the Angles in a Triangle Sum up to 180 Degrees

We are taught that the sum of the angles in a triangle add up to 180° Here is a simple way to demonstrate that fact. A proof of the angles of a triangle summing to 180° can be found here. Materials paper pencil or pen ruler (or some sort of straight-edge) coloured crayon scissors 1) […]

Mathematics

Proving the Pythagorean Theorem

We learned the Pythagorean Theorem in grade school: The square of the length of the hypotenuse is equal to the sum of the squares of the other two sides. Often written as A2 + B2= C2. The Pythagorean Theorem is much more than just a mathematical curiosity, it is a basic and useful mathematical property […]