Solving arithmetic problems could be pretty easy, especially when you have basic math knowledge. However, when math specializations come into the picture, how will you be able to predict, for instance, the exact curve of a function using only a pen, paper, and your mind, in less than a minute?
Back in the ancient times, before the Hindu-Arabic numeral system was established, a calculating tool known as the abacus was used. This counting frame is characterized by beads manipulated by the fingers to perform simple addition, subtraction, multiplication, division, and extraction of square roots and cubic roots. When 1642 came, the first true calculator was invented by Blaise Pascal, which performed simple calculations with a mechanism resembling a clockwork.
Solving mathematical problems has been a lot easier since a compact computer, in the form of calculators, have existed. Calculators have had their fair share of evolving history, and, today, they come in three main types – basic, scientific, and graphing. Among these three, graphing calculators seem to top the list for the most number of functions and uses. You can also find a number of tools available online such as a derivatives calculator, matrix calculators, among others.
Graphing Calculators: What Are They?
Before directly delving into the wonders of a graphing calculator, it might be a helpful step to introduce it first. Unlike the basic and scientific calculators, graphing calculators are instruments that perform fundamental math processes that basic and scientific ones can do, but they can do so much more. Graphing calculators are also capable of solving mathematical equations at the same time, plotting lines and graphs, and playing with several variables.
If you’re reading this right now, great chances are you’re trying to find a new graphing calculator for the new semester. Whether you’re a new user or simply repurchasing another one, you deserve to know the best graphing calculator in the market, including their best features and on how to use them to their advantage. Some of the best features that graphing calculators possess are the following:
- Large Display: Many graphing calculators have large displays that allow simultaneous showing of numerous lines of text, calculations, and figures. Since they’re labelled as calculators that can do graphing and plotting, they have screens big enough to show the entirety of lines and curves.
- Programmable: For advanced users, this feature is highly beneficial. You can write your own programs and systems and store them in the calculator, thus every time you’ll be needing, say, a complicated formula you always tend to forget, it’s pretty straightforward and quick to find it.
- Additional Advanced Features: New models of graphing calculators today can be connected to the Internet and computer to amplify their functionality. Moreover, you can also connect it with instruments, like weather devices, pH gauges, electronic thermometers, and electronic accelerometers, to serve as data loggers.
Graphing Calculator: How Is It Used In Different Fields?
Graphing calculators show more of their abilities once you start using them in different disciplines for which they’re created. Some of these advanced disciplines might not ring a bell to you now, but, sooner or later, you’re going to encounter them once you further your math studies.
Trigonometry
While trigonometry is usually an elective or optional subject for middle schoolers, using graphing calculators for trigonometry can be entirely useful for people who pursue higher mathematics, as well as for professionals like chemists, architects, statisticians, software developers, and more. In short, trigonometry is an essential subject in many careers due to its innovative real-life applications. Trigonometry focuses on triangles and its angles and dimensions. It might sound like a simple discipline that revolves around these three-sided figures, yet it’s used in many foundations of engineering, architecture, and other related fields.
If you’re just starting out, you’ll not be allowed to use scientific and graphing calculators as you have yet to grasp the basic concepts of trigonometry. However, as you dive deeper and deal with applications involving trigonometry, your graphing calculator can be used for:
- Solving and graphing trigonometric equations
- Graphing basic trigonometric functions
- Degree to radian conversions and vice versa
- Graphing asymptotes
- Sinusoidal functions and graphs
- Inverse trigonometric functions
- Verifying trigonometric identities
- Law of sines and cosines
Statistics
Statistics is an essential field in mathematics, dealing with collecting, analyzing, interpreting, and presenting various forms of data. Without statistical techniques, data analysis would take longer time to do. With the help of graphing calculators, you can analyze and interpret data and arrive at your desired results in an instant.
Here’s how graphing calculators can be used in statistics:
- Spreadsheet input and formula applications
- Getting descriptive statistics, which involves:
- Typing data into tables
- Finding the weighted means
- Estimating the mean and standard deviation based on frequency distributions
- Creating statistical illustrations, such as line charts, histograms, scatter plots, box plots, and more, according to input data
- Finding confidence intervals based on standard normal distribution in z-interval or the t-distribution in t-intervals
- Hypothesis testing
- Finding normal and binomial probabilities
Scientific calculators probably have all the functions and features that you’re going to need in a typical stats class, yet graphing calculators can make your life easier due to their advanced functions.
Geometry
Unlike trigonometry, which only deals with triangles, geometry is a sub-branch of mathematics that generally encompasses both two-dimensional and three-dimensional shapes and everything about them. Geometry contributes in people’s daily lives in such a way that it helps them to know how much resources are needed in order to meet daily demands, how to minimize or maximize them, how to measure these resources according to what’s needed, and to turn visual imaginations into reality.
There are also numerous ways on how graphing calculators can be used in geometry. Whether you’re dealing with geometry classes next semester or pursuing a geometry-related studies, here are ways on how you can use your calculating tool:
- Examining transformations
- Reflection over x and y axes
- Reflection when coordinates are interchanged
- Reflection in origin
- Translations
- Dilations
Since geometry has more to do with spatial and visual interpretations, it has numerous real-life applications used in architecture, art, anthropology, and technology. Graphing calculators are great tools for designing plans, blueprints, and software by applying the principles of transformations and related concepts.
Engineering
Technical students turned into successful engineers of different fields today have always relied on graphing calculators. The field of engineering – civil, chemical, electrical, geotechnical, mechanical, and management – is a complex endeavour requiring engineers to apply scientific concepts onto bigger scales, create new designs of things, and solve problems. The many uses of graphing calculators mentioned above can be pretty summed up into the field of engineering, that’s why it’s a big must for engineering students and professionals to always have a graphing calculator with them.
A broad selection of engineering applications can be performed through the following functions of graphing calculators:
- Large display with numerous memory codes, important for storing data and formulas to be used later
- Periodic table of elements, with corresponding information
- Conversion units
- Limits, differentiation, and integration functions
Finance
Business and finance are two essential components that work hand in hand to make today’s world revolve sustainably. The two make sure that markets have enough funds to operate and invest, and, at the same time, ensure that every venture is running smoothly and efficiently through playing with funds.
Below are surprising ways on how graphing calculators can be used in finance, despite the fact that graphs and money seemingly don’t have anything to do with each other:
- Basic financial applications involving Time Value for Money (TVM), including calculations for:
- Payment on an annuity
- Number of periods
- Present value of investment
- Amortization schedules
- Present and future values
- Interest rates
- Mixed cash flows
- Present and future values of annuities
- Interest rate, time, and payment of annuities
- Non-annual compounding and discounting
- Bonds
- Amortization
- Net present values (NPV)
- Internal rates of return (IRR)
Graphing calculators allow students and professionals alike to combine multiple financial calculating tools into one powerful portable computer. Even if you don’t have access to data connection or Wi-Fi, you still can solve financial problems in an instant with the help of graphing calculators.
Computer Programming
As mentioned in the first part, a unique feature of graphing calculators that sets them apart from basic and scientific calculators is its ability to become programmable, meaning the user can write and store programs in them, and use those programs anytime for solving problems or to run complex procedures. If you’re merely starting with computer programming, the best thing to do is to immerse yourself into calculator programming with the help of graphing calculators.
The Bottom Line
Graphing calculators possess features that are beneficial when traversing the path of mathematics and its various branches, such as trigonometry, geometry, and even in the fields of engineering, finance, and computer programming. Their amazing functionality lets students and professionals perform various mathematical equations and processes without even breaking a sweat. However, graphing calculators available in the market today aren’t created equal, so expect that some of them will have variations in functions and buttons.
Because of hand-held graphing calculators, anyone can make numerous possibilities even without the presence of a computer, anytime and anywhere.
