STEM Creations

Logarithms helps us represent large numbers in very compact form. It can also be used to tell us how many of one number we must multiply to get another number. The exponential function y=a^x is one of the most important functions in mathematics, physics, and engineering. Applications relating to radioactive decay, bacterial growth, population growth, continuous interest all involve exponential functions. We know that logarithmic and exponential functions are inverses. This means one can chan

In this document, the students will learn about the graphs of several trigonometric functions. These are the graphs of sine, cosine, and tangent functions. They will learn how the graphs of y=sin(θ), y=cos(θ), y=tan(θ) and their reciprocals look. It is essential that they also practice how to graph these functions on their own.

Solving trigonometric equations requires one to be be able to know how use reference angles, inverse trigonometric function ideas along with several algebra ideas. In short, the main principles often applied in solving trigonometric equations include 1. principle of zero products 2. Principle of square roots 3. Factorization 4. Identities 5. The unit circle 6. The Quadratic formula 7. etc.

This document describes in detail the basic concept of projectile motion. When an object is thrown above the ground with an initial velocity u at an angle to the ground, it experiences projectile motion. In a vacuum, the only force acting on the object would be the downward gravitational force. The projectile motion is such that the horizontal velocity (V_x) stays constant while vertical velocity (V_y) shows that the object will decelerates until it reaches the maximum height, and then accelera

How to prove Trigonometric Identities An identity is an equation that is known to be always true. To prove a trigonometric identity follow these suggested guidelines: 1. Pick a side that is easy to transform. Pick the left-hand side (LHS) or the right-hand side (RHS) 2. Use algebra or basic trigonometric identities to transform one side to another. 3. If it is possible, express the entire equation in terms of one trigonometric function 4. If it is possible, express the side chosen in terms of s

In this article, I describe some very simple steps that can be used by any student to find all the six trigonometric ratios for special angles. The angles are 0, 30, 45, 60 and 90 degrees. The angles can also be given in radians. Our method can augment the unit circle very well. The method described is rarely taught in schools but very useful!

OBJECTIVES 1. The student should be able to express quadratic equations in standard form: ax^2 + bx+c =0 and be able to extract the numbers, a, b and c. 2. The student should be able to find the discriminant, D= b^2 - 4ac in the quadratic formula and be able to identify the three types of solutions that one can get when solving a quadratic equation. 3. The student should be able to solve quadratic equations by using the quadratic formula.

OUTLINE In order to multiply and simplify two rational expressions: 1. Factor each numerator polynomial and multiply out the factors 2. Factor each denominator polynomial expression and multiply out the factors 3. Apply the fundamental principle of fractions by dividing the common factor or factors. 4. The simplest form will be the quotient of the product of remaining

The value of a trigonometric function of an angle equals the value of the cofunction of the complement of the angle. In this article, we show the cofunction relationships of all the six trigonometric ratios.

At the end of this lessons, the students should be able to mimic the steps involved in the long division of polynomials. ------------------------------------ STEPS required for Dividing by a Polynomial Containing More Than One Term during long division: Step 1: Express the polynomial being divided out with terms of descending order of powers. If any terms are missing, use a zero to fill in the missing term. Step 2: Divide the term with the highest power inside the division symbol by the term

OUTLINE 1. Express the polynomial in standard form 2. Write out the coefficients of the polynomial, ensuring that a zero is placed appropriately as coefficients for missing degrees of the polynomial 3. Solve the binomial divisor equal to zero 4. Apply the multiply and add Patterns 5. The remainder from the division is the result from the last column of the add patterns. 6. If this remainder is a zero, then the divisor is a factor of the polynomial

Beer's Law (Beer-Lambert Law): The amount of energy absorbed or transmitted by a solution is proportional to the solution's molar absorptivity and the concentration of solute. In simple terms, a more concentrated solution absorbs more light than a more dilute solution does. The mathematical statement of Beer's law is A = εlc, where: A = absorption; ε = molar attenuation coefficient, l = path length (the thickness of the solution), and c = concentration of the solution. This equation is also exp

At the end of the lesson, the student should be able to recognize polynomials that are a sum or difference of cubes and be able to factorize them. A polynomial in the form A^ 3 + B^3 is called a sum of cubes. When factored, A^ 3 + B^3 = (A+B)(A^2 - AB + B^2) A polynomial in the form B^3 – B^ 3 is called a difference of cubes. When factored, A^ 3 - B^3 = (A-B)(A^2 + AB + B^2)

To transform a graph of a function means to shift its graph to the left or right hand side, stretch/shrink vertically or horizontally, or to reflect its graph across the x-axis or the y-axis. In this document, the students will learn about what it means to transform sine and cosine functions. Illustrated examples are also given.

OUTLINE In order to Simplify a rational expression, follow these steps: 1. Completely factor the polynomials given in the numerator and denominator of the rational expression. 2. Apply the fundamental principle of fractions by dividing the common factor or factors. If necessary, the properties of exponents can also be applied. 3. The simplest form will be the quotient of the product of remaining expressions.

OUTLINE In order to divide and simplify two rational expressions: 1. Multiply the first rational expression by the reciprocal of the second rational expression. 2. Factor each numerator polynomial and multiply out the factors 3. Factor each denominator polynomial expression and multiply out the factors 4. Apply the fundamental principle of fractions by dividing the common factor or factors. 5. The simplest form will be the quotient of the product of remaining expressions

This document describes how one can efficiently determine the sign of each trigonometric function in each quadrant.

OBJECTIVES: At the end of this lesson: 1. The students should able to name the parent functions. 2. The students should able to name the parent functions.