In this article, you will learn how to use each double angle formula for sine, cosine, and tangent in simplifying and evaluating trigonometric functions and equations. This article also includes double angle formulas proof and word problems.
Learn how to solve direct variation examples. This article also includes a definition of direct variation, as well as the corresponding formula, graph, and an explanation of how to create formula equations.
This article will teach you how to find coterminal angles in degrees and radians.
Learn about three ways of solving quadratic equations in this quick maths article.
Learn how to solve inverse variation problems in algebra. This article also includes definitions, formulas, graphs, and examples explaining how to translate mathematical statements of inverse variations to equations and vice versa.
Learn how to solve joint variation problems in algebra. This article includes definitions and various examples about joint variation and combined variation that will help gauge understanding of the topic.
Learn how to calculate the area of the shaded region using the area decomposition method. This article also includes step-by-step procedures for all types of problems involving shaded areas.
Learn how to sketch a cotangent graph by learning its properties such as period, horizontal shift, vertical shift, amplitude, vertical asymptotes and more. This article also includes examples of step-by-step procedures on how to graph secant functions with different forms.
Learn how to sketch a secant graph by learning its properties such as period, horizontal shift, vertical shift, amplitude, and more. This article also includes examples of step-by-step procedures on how to graph secant functions with different natures.
Learn the different reciprocal identities in trigonometry together with other fundamental identities such as Pythagorean and quotient identities. This article includes several examples that can help in understanding the trig reciprocal identities.
Learn how to apply sum and difference formulas in solving trigonometric equations. This article also includes the definition of sum and difference identities, proofs, and examples with solutions.
Learn how to solve problems about similar polygons using the concepts of ratio of areas, perimeters, side lengths, diagonals, and angle bisectors. This article also includes practice problems with solutions and answers that will help gauge understanding of the topic.
You keep pulling socks out of a messy drawer, desperately trying to find a matching pair, but all you seem to get are odd socks. How many socks will you need to pull out of the drawer in order to be guaranteed a matching pair? Find out in this quick mathematics article.
Learn how to solve mutually inclusive events in probability by going through the examples written in this article.
Learn how to use the triangle proportionality theorem to complete triangle proportions, solve word problems, and find the value of the missing sides of a triangle. This article includes the triangle proportionality theorem proof and examples that can help you fully gauge your understanding of it.
A look at how using the difference of two squares can speed up your mental arithmetic with large numbers
It's common knowledge that the square root of two is an irrational number, but how can we prove it? Find out in this quick mathematics article.
Learn how to rationalise the denominator in this quick high school mathematics article.
When learning about surds/radicals at school, we are always told to rationalise the denominator. But what does this mean and why do we do it? Find out why in this quick mathematics article.
Two criminals have been arrested for a crime, but the police don't have enough evidence to convict. They offer each criminal the chance to reduce their sentence by testifying against the other, but is this the best option? Find out in this quick math article.
The village of Smallville and the Intergalactic Gods have both had five metres of boundary rope stolen from their circular cricket pitches. They have vastly different sized pitches, so whose pitch will reduce in radius the most?
Alan has the best scoring average in the first half of the basketball season and the best scoring average for the second half of the season, but when everything is tallied together he finds that it is Brian who has the highest average over the season. Find out how in this quick math article.
This article will provide a look at Hilbert's Paradox of the Grand Hotel, also known as the 'Infinite Hotel Paradox'. Find out how to fit extra guests into the infinite hotel, even when every room is occupied!
Learn how to evaluate and simplify the limits of indeterminate forms using L'Hopital's Rule. This article includes L'Hopital's Rule Proof, when to use it, and examples with solutions about finding the limit of various functions.
This article includes problems with solutions teaching how to convert rectangular to cylindrical coordinates and vice versa, identify the surfaces in the cylindrical coordinate system, and find a cylindrical equation of three-dimensional spaces.
Learn how to use the Divergence Test in determining the convergence or divergence of a series.
Learn how to solve the derivative of constant times a function through a step-by-step Constant Multiple Rule method.
Learn how to solve problems about cofunction identities in trigonometry. This article also includes formulas, proofs, and examples with solutions that can help you fully apply the cofunction trigonometric identities.
Learn how to find the linear approximation or differentials of a function at a given point. This article also includes formulas, proof, and examples with solutions that can help you fully understand the Linear Approximation topic in Calculus.
The slope of a line is the direction in which the line goes. You can calculate it as the ratio between horizontal change and vertical change, or you can use the derivative.
Finding the intersection is something that comes up a lot in math. To do this you need to set the expressions equal and solve for x. Then you can determine y by filling in the x you found.
The variance of a probability distribution is a measure to quantify the spread of a distribution. If the variance is low, all outcomes are close to the mean, while distributions with a high variance have outcomes that could be far away from the mean.
The mean is the most important measure of probability distributions. It tells a lot about the likelihood that certain events will happen.
If you were asked to add together all of the numbers from 1 to 100, what would you do? Would you go through each number, adding to your total as you went or is there a quicker way? Find out in this article.
A right triangle is a triangle in which one angle is right, meaning it is exactly 90°. For these triangles, it is possible to calculate the other angles using goniometric functions as the sine, cosine and tangent.
The limit of a function describes how the function behaves in the neighborhood of some value. Often, it is interesting to look at the limit for x to infinity. This describes what happens when you would follow the line of the graph of the function until "the end".
Finding the minimum or maximum of a function is very important in mathematics. It can help you finding the optimal solution to a problem. Often you want some quantity to be maximal, such as profits or capacity. Also minima can be very useful, for example, when looking at a cost function.
Finding the derivative is something that comes up a lot in maths, but what is it actually? The derivative tells you what the slope of the function is in a certain point. The derivative of a function can be calculated using the definition, but mostly it is done by using standard rules.
In this article, you can learn how to use the power-reducing formulas in simplifying and evaluating trigonometric functions of different powers.