Simplifying Algebraic Expressions on TI 89 Titanium Calculator

Brian G
22 Feb 201503:08

TLDRThis video demonstrates simplifying algebraic expressions using the TI 89 Titanium calculator, highlighting its power for solving complex equations with ease. The video covers two questions from a test, showing that over half of the students struggled with them. However, with the calculator, these problems can be solved instantly by inputting the equations and pressing enter, resulting in simplified answers. The first simplifies to 2*cos(x), and the second to 1/x^2, proving the calculator's efficiency in mathematical problem-solving.

Takeaways

  • 🧮 The video demonstrates how to simplify algebraic expressions using the TI-89 Titanium calculator.
  • 📊 The TI-89 calculator can solve complex math problems by simply entering the equation and pressing 'Enter'.
  • 🧑‍🏫 The example shows a simplification problem involving trigonometric functions: `sin(x) + sin(-x) + cos(x) + cos(-x)`.
  • 🔍 By entering the trigonometric equation into the TI-89, it simplifies directly to `2 * cos(x)`, which matches choice D.
  • ✅ The calculator does all the work, requiring no manual calculations, making it very efficient.
  • 📐 The second example involves simplifying a factorial expression: `(n-1)!^2 / n!^2`.
  • 🔢 The video advises replacing `n` with `x` for ease of input into the calculator.
  • 📝 The factorial key can be found in the calculator's catalog, and expressions must be carefully keyed in with proper parentheses.
  • 🧩 Entering the factorial expression in the calculator results in `1/x^2`, equivalent to `1/n^2`, matching choice B.
  • 👍 The video emphasizes how the TI-89 makes complex mathematical simplifications easy and quick, showcasing its effectiveness.

Q & A

  • What is the main topic of the video?

    -The main topic of the video is simplifying algebraic expressions on the TI 89 Titanium calculator.

  • Why does the speaker consider this video one of their favorites?

    -The speaker considers this video one of their favorites because it demonstrates the power of the TI 89 calculator in simplifying equations, which the college board allows to be used on the test.

  • What percentage of students got the first question right according to the video?

    -According to the video, 56 percent of students got the first question right.

  • What is the equation given in the first question of the video?

    -The equation given in the first question is sine x plus sine negative x plus cosine x plus cosine negative x.

  • What does the TI 89 calculator simplify the equation to, and which choice does it correspond to?

    -The TI 89 calculator simplifies the equation to 2 cosine x, which corresponds to choice D.

  • What is the second simplification problem discussed in the video?

    -The second simplification problem is n minus 1 factorial squared divided by n factorial squared.

  • How does the speaker suggest simplifying the second problem for ease of use on the calculator?

    -The speaker suggests using x instead of n for simplicity when inputting the problem into the calculator.

  • What is the key used to input factorial in the calculator, according to the video?

    -According to the video, the factorial key is found in the catalog under the exclamation mark.

  • What is the simplified result of the second problem, and which choice does it correspond to?

    -The simplified result of the second problem is 1 over x squared, which corresponds to choice B.

  • How does the speaker describe the ease of using the TI 89 calculator for these problems?

    -The speaker describes the ease of using the TI 89 calculator as 'easy peasy,' emphasizing that no work is needed other than entering the equation and pressing enter.

  • What is the speaker's opinion on the difficulty of the questions presented in the video?

    -The speaker's opinion is that the questions are not difficult at all, as they can be easily solved using the TI 89 calculator without any math.

Outlines

00:00

📚 Simplifying Equations with TI-89 Calculator

This paragraph introduces a video tutorial on simplifying equations using the TI-89 calculator. The speaker expresses enthusiasm for the topic, suggesting that the TI-89's capabilities are underutilized, especially in the context of standardized testing. The video aims to demonstrate how the calculator can simplify two specific equations with minimal mathematical input from the user. The first equation involves trigonometric functions, and the second is a factorial-based simplification problem. The speaker emphasizes the ease of use, stating that the calculator does the work, simplifying the equations to their most basic forms.

Mindmap

Keywords

💡Simplifying

Simplifying refers to the process of making something easier to understand or use, especially by reducing it to its simplest form. In the context of the video, simplifying algebraic expressions means reducing complex equations to a more straightforward form. The TI 89 Titanium calculator is shown to be a powerful tool in this process, as it can automatically simplify equations with a simple input and press of a button, as demonstrated in the script.

💡TI 89 Titanium Calculator

The TI 89 Titanium Calculator is a high-performance graphing calculator used for various mathematical computations, including algebraic simplification. It is favored for its advanced capabilities, such as simplifying equations without the need for manual calculations. The video emphasizes its utility in solving algebraic problems, showcasing how it can simplify equations with ease, which is a central theme of the video.

💡Algebraic Expressions

Algebraic expressions are mathematical phrases that consist of variables, numbers, and operators (like addition, subtraction, multiplication, and division). The video script discusses the simplification of these expressions using the TI 89 calculator, highlighting the calculator's ability to reduce complex algebraic expressions to simpler forms, which is a key aspect of the demonstration.

💡College Board

The College Board is an organization that develops and administers standardized tests and curricula used by K-12 and post-secondary education institutions. In the video, the presenter mentions the College Board in the context of its policies regarding the use of calculators in exams, suggesting that the TI 89's capabilities might be underutilized or misunderstood in the context of these exams.

💡Sine Function

The sine function is a trigonometric function that relates the ratio of the length of the opposite side to the length of the hypotenuse in a right-angled triangle. In the video, the sine function is used in an algebraic expression that the TI 89 calculator simplifies. The script provides an example of inputting sine of an angle and its negative counterpart into the calculator.

💡Cosine Function

The cosine function, like the sine function, is a trigonometric function that relates to the angles of a right-angled triangle. It is used in the video script to demonstrate the simplification of an algebraic expression involving both sine and cosine functions, showing how the calculator can simplify the expression to 2 times the cosine of the angle.

💡Factorial

A factorial, denoted by an exclamation mark (!), is the product of all positive integers up to a given number. In the video, the concept of factorial is used in an algebraic expression that the TI 89 calculator simplifies. The script explains how to input and square a factorial in the calculator, which is a crucial step in solving the problem presented.

💡Squaring

Squaring is the mathematical operation of multiplying a number by itself. In the context of the video, squaring is used to transform an expression or a factorial, as shown when the script describes squaring the expression (x - 1) factorial divided by x factorial squared, leading to the simplification of the expression.

💡Catalog

In the context of the TI 89 calculator, the catalog refers to the menu or list of functions and operations available on the device. The video script mentions using the catalog to find the factorial function, which is necessary for inputting and simplifying the algebraic expressions discussed.

💡Simplification Problem

A simplification problem is a type of mathematical problem that requires reducing a complex expression to a simpler form. The video script presents two such problems, demonstrating how the TI 89 calculator can be used to solve them with minimal effort, emphasizing the ease and efficiency of using the calculator for this purpose.

💡Equation

An equation is a statement that two expressions are equal, often used in mathematics to represent a relationship between variables. In the video, equations are the core of the simplification problems presented, and the TI 89 calculator is shown to be capable of simplifying these equations to reveal their underlying relationships.

Highlights

This video demonstrates simplifying algebraic expressions using the TI 89 Titanium calculator.

The presenter discusses the potential for the TI 89 calculator to be underutilized in exams.

Only 56% of students answered the first question correctly, indicating potential difficulty.

The TI 89 can simplify equations with no mathematical work required by the user.

The first equation simplifies to 2 cosine x, which is choice D.

Sine of negative x and cosine of negative x are shown to simplify using the calculator.

The presenter emphasizes the ease of inputting and simplifying equations on the TI 89.

The second question involves factorials and their simplification.

Using the TI 89, factorials can be inputted and simplified with ease.

The equation n - 1 factorial squared over n factorial squared simplifies to 1 over x squared.

The presenter shows the process of finding the factorial key in the calculator's catalog.

Parentheses and squaring operations are crucial for accurate simplification.

The final answer for the second question is choice B, 1 over n squared.

The video highlights the simplicity and efficiency of using the TI 89 for algebraic simplification.

The presenter suggests that the TI 89's capabilities are not fully recognized in educational settings.

The video concludes by reiterating the ease of using the TI 89 for complex simplification tasks.