Brian McLogan
Pre-Calculus - Find All of the Solutions of an Equation Using the Double Angle Formulas
👉 Learn how to use the double angle identities to solve trigonometric equations. When we have equations with a double angle we will apply the identities to create an equation that can help solve by inverse operations or factoring. We...
Brian McLogan
Learn how to find the angle between two vectors
Learn how to determine the angle between two vectors. To determine the angle between two vectors you will need to know how to find the magnitude, dot product and inverse cosine. Then, the angle between two vectors is given by the inverse...
Brian McLogan
How to determine the resultant vector algebraically and geometrically
Learn how to add/subtract vectors. Vectors can be added, subtracted and multiplied. To add or subtract two or more vectors, we simply add each of the corresponding components of the vectors.
Brian McLogan
Evaluate the left hand limit
👉 Learn how to evaluate the limit of a function involving rational expressions. The limit of a function as the input variable of the function tends to a number/value is the number/value which the function approaches at that time. The...
Brian McLogan
How do you understand the direction of an angle
Learn how to determine the magnitude and direction of a vector. The magnitude of a vector is the length of the vector. The magnitude of a vector is obtained by taking the square root of the sum of the squares of the components of the...
Brian McLogan
Learn how to add two vectors and graph their result
Learn how to add/subtract vectors. Vectors can be added, subtracted and multiplied. To add or subtract two or more vectors, we simply add each of the corresponding components of the vectors.
Brian McLogan
Learning the quick way to rotate a point 90 degrees counter clockwise
👉 Learn how to rotate a figure and different points about a fixed point. Most often that point or rotation will be the original but it is important to understand that it does not always have to be at the origin. When rotating it is also...
Brian McLogan
Learning how to reflect a polygon over the x=y line
👉 Learn how to reflect points and a figure over a line of symmetry. Sometimes the line of symmetry will be a random line or it can be represented by the x or y-axis. Either way when reflecting a point and or figure over the line of...
Brian McLogan
How To Write a Proof - Proving Parallel Lines
👉 Learn how to write a proof when given angles from parallel lines and a transversalWe will explore angle relationships with parallel lines and a transversal. Parallel lines are two lines on a plane that will never intersect and a...
Brian McLogan
Given a list of zeros, learn how to write the equation of a polynomial
👉 Learn how to write the equation of a polynomial when given rational zeros. Recall that a polynomial is an expression of the form ax^n + bx^(n-1) + . . . + k, where a, b, and k are constants and the exponents are positive integers. The...
Brian McLogan
How do you expand logarithmic expressions
👉 Learn how to condense/expand logarithmic expressions. A logarithmic expression is an expression having logarithms in it. To condense logarithmic expressions means to use the logarithm laws to reduce logarithm expressions from the...
Brian McLogan
Write the domain in interval notation of a rational function
👉 Learn how to find the domain of rational functions. Recall that the domain of a function is the set of possible input values (x-values) of the function. For a rational function, the denominator cannot be zero. Thus, to find the domain...
Brian McLogan
How to use the chain rule with a square root
👉 Learn how to find the derivative of a function using the chain rule. The derivative of a function, y = f(x), is the measure of the rate of change of the function, y, with respect to the variable x. The process of finding the derivative...
Brian McLogan
How does the fixed point affect our rotation
👉 Learn how to rotate a figure and different points about a fixed point. Most often that point or rotation will be the original but it is important to understand that it does not always have to be at the origin. When rotating it is also...
Brian McLogan
Solve a system of linear equations using substitution
👉Learn how to solve a system of equations by substitution. To solve a system of equations means to obtain a common values of the variables that makes the each of the equation in the system true. To solve a system of equations by...
Brian McLogan
Summary for solving and graphing compound inequalities
👉 Learn all about solving and graphing compound inequalities. An inequality is a statement in which one value is not equal to the other value. A compound inequality is a type of inequality comprising of more than one inequalities. To...
Brian McLogan
Solving a linear equation with infinite many solutions
👉 Learn how to solve multi-step equations with parenthesis and variable on both sides of the equation. An equation is a statement stating that two values are equal. A multi-step equation is an equation which can be solved by applying...
Brian McLogan
Learn how to use mathematical induction to prove a formula
👉 Learn how to apply induction to prove the sum formula for every term. Proof by induction is a mathematical proof technique. It is usually used to prove that a formula written in terms of n holds true for all natural numbers: 1, 2, 3, ....
Brian McLogan
Evaluate the sum of two angles with cosine
👉 Learn how to evaluate the cosine of an angle in radians using the sum/difference formulas. To do this, we first express the given angle as a sum or a difference of two (easy to evaluate) angles, then we use the unit circle and the...
Brian McLogan
Learn how to apply the dot product between two vectors
Learn how to determine the dot product of vectors. The dot product of two vectors also called the scalar product of the vectors is the sum of the product of the components of the vectors in each direction. When the magnitudes of the...
Brian McLogan
Graphing and finding the difference of two vectors
Learn how to determine the resultant vector by adding, subtracting and multiplying vectors by a scalar. We will also learn how to graph the resultant vectors to show the operations. Vectors can be added, subtracted and multiplied. To add...
Brian McLogan
Evaluate a limit at infinity with a radical in denominator
👉 We will explore how to evaluate the limit at infinity. When evaluating the limit at infinity or negative infinity we are interested to know where is the graph going right and left. This is also commonly explored as end behavior of the...
Brian McLogan
Given a Irrational Factor | Find All the Zeros of the Polynomials
👉 Learn how to find all the zeros of a polynomial given one irrational zero. A polynomial is an expression of the form ax^n + bx^(n-1) + . . . + k, where a, b, and k are constants and the exponents are positive integers. The zeros of a...
Brian McLogan
How to apply the operations of dot product to a vector
Learn how to determine the dot product of vectors. The dot product of two vectors also called the scalar product of the vectors is the sum of the product of the components of the vectors in each direction. When the magnitudes of the...