Students in high school and the early stages of college are frequently required to take a trigonometry class.
Trigonometry is used to calculate unknown lengths and angles. Unfortunately, learning this field of mathematics is also difficult.
It is not uncommon for pupils to struggle greatly when they are initially introduced to it. Here are ten reasons why trigonometry can be difficult to master.
Is Trigonometry Difficult? (10 Reasons Why it Could Be)
One of the reasons trigonometry is difficult is that it employs functions. Functions are used in almost every sort of arithmetic, but the functions used in trigonometry are exceptionally complex.
This is due to the fact that there are six core functions that branch off to produce a succession of secondary functions.
The student must study and memorize all of these different functions in order to calculate various angles and lengths.
They will never be able to solve the problem if they cannot recall a specific function or variation of a function.
It is not as simple as basic algebra. There are only a few rules to know when it comes to math.
Trigonometry requires you to recall terms like sine and cosine. You must remember what they represent and how they affect angles and lengths.
Trigonometry is challenging since it requires a great deal of knowledge of many functions that might subsequently diverge into other functions.
The fact that trigonometry is non-linear is probably the most difficult aspect of it. The arithmetic is rather simple using basic algebra. You must solve for X.
While this occasionally necessitates working on both sides of the problem, it is still a very linear procedure.
Trigonometry is not a linear subject. That’s because everything revolves around a circle. A circle isn’t a straight line.
This elevates trigonometry to a higher level of math, requiring the individual to think beyond a fundamental linear form.
This is complicated. The student must comprehend how a circle divides into distinct angles.
Then kids must comprehend how those angles interact to produce distances and other angles.
In a non-linear way, the arithmetic might become exceedingly complicated. This makes trigonometry extremely difficult to grasp.
3. The Unit Circle
Trigonometry is all about the unit circle. Students will be unable to learn additional trigonometry ideas if they do not understand how a unit circle works or what it looks like.
This makes the math challenging because it is dependent on a student’s ability to recall how a unit circle works.
A unit circle is, in essence, a circle with a radius of one. When the radius exceeds one, trigonometry gets incredibly difficult and sophisticated.
When building a unit circle, the center of the circle is placed on a graph where the X and Y axes intersect. The sine and cosine values are then defined by the unit circle.
When executing trigonometric functions, you rely on the unit circle to help you calculate various sine and cosine values. Sine does not have the same value for each angle.
Trigonometry is difficult because it employs a unit circle, which adds to the difficulty of this subject of mathematics.
4. Radians and Degrees
It is not sufficient for kids to solve degrees using trigonometry. As the math becomes more complicated, pupils must also convert their solutions into radians.
The radian is a pure measure whose foundation is the radius of the unit circle. A single radian is the angle formed when the radius wraps around the unit circle.
One radian is approximately 57.2958 degrees. This is due to the fact that while employing radians, degrees are replaced by the pi symbol ().
You also use pi for the majority of the calculations. Pi creates unclean solutions since it is not a clean number. Converting degrees to radians is both simple and difficult.
The formula itself is straightforward, but if something else goes wrong in your computations, it’s easy to miscalculate the entire thing.
To convert from radians to degrees, multiply your answer by 180, then divide by pi. If you want to convert your degrees to radians, multiply your result by and then divide it by 180.
Radians are necessary for obtaining a more precise response. The radian is the chosen unit to use when planning architecture or doing surveys since it is more accurate than degrees.
However, the fact that you can’t just take the solution in degrees as it complicates trigonometry.
Trigonometry is difficult because the final answer you obtain while performing your calculations may not be the final answer at all.
You may need to convert it into a different unit, which adds another layer of complexity and increases the likelihood of getting the answer wrong.
5. Memorization of Recognized Values
To execute trigonometric calculations, you must memorize a few known values. When calculating in degrees for a unit circle, you must know the correct values of sine, cosine, and tangent.
These are not actual figures. Instead, they are functions. They also differ depending on the degree to which you are working.
The value of sine at 30 degrees, for example, is 1/2. The value of sine at 45 degrees, on the other hand, is the square root of two divided by two.
There’s one more thing you should know about sine. At 60 degrees, sine is the square root of three divided by two.
These values are shared by the other functions as well. The sine at 60 degrees is the same as the cosine at 30 degrees. The answer is the square root of three divided by two.
Because you have numerous values to remember, and those values are similar to some extent to the other functions, it’s simple to get them jumbled up.
If you mix them together, your math will be completely thrown off. Degrees aren’t the only thing you’ll need to remember.
You must also keep in mind their radian counterparts. A radian value of 30 degrees, for example, is divided by six.
The radian value of 60 degrees is divided by three. This continues until you reach 360 degrees, which has a radian value of 2 multiplied by.
Trigonometry is difficult since you must learn numerous values of distinct functions in both degrees and radians. If you don’t recall them or mix them up, your calculations will be inaccurate.
6. Cartesian Coordinate Rules
Another reason trigonometry is difficult is that it is based on the Cartesian Coordinate principles.
Students may only have a limited understanding of how to produce trigonometric functions if they do not comprehend how these rules work.
Cartesian coordinates simply indicate the location of a point on a map or graph. They are calculated by identifying the point’s location on a graph and how far along it is.
As an example, consider the coordinates of (12, 2). This tells us that the graph point is 12 units along the X-axis and 2 points up the Y-axis.
However, while initially learning about Cartesian coordinates, it is common to make mistakes. Students must particularly acquire and comprehend the concept of an ordered pair.
An ordered pair denotes that the numbers must be in a specified order. The ordered pair is based on the first number representing the X-axis and the second number representing the Y-axis in Cartesian coordinates.
It is usually spelled as (X, Y). As an example, a coordinate of (12, 2) indicates that the point on the graph has an X-coordinate of 12 and a Y-coordinate of 2.
If pupils mix them up—for example, forgetting that the 2 is with the Y and writing it with the X—then the basic foundations of all trigonometric computations in the future will be erroneous.
Cartesian coordinates can become complicated as well. They can have negative values. For example, students may notice the coordinate (5, 12).
This signifies that the point on the graph is on the X-coordinate five units to the left rather than the right.
Because the Y-coordinate is still positive, it indicates that it is still near the top of the graph rather than below it.
A negative number denotes the crossing of that coordinate’s line. If an X-coordinate is negative, it will cross the X-axis to the left side.
If a Y-coordinate is negative, it will cross the Y-axis to the bottom of the graph. Including negatives might make reading or computing values from the graph even more challenging.
Trigonometry is difficult because it uses Cartesian coordinates, which are easy to miscalculate at first.
7. Polar Coordinates
While Cartesian coordinates are required for an early comprehension of trigonometry, polar coordinates are used for the majority of the math.
A two-dimensional coordinate system is polar coordinates. It employs r and theta () as units instead of X and Y.
These are the distance from a reference point (r) and the angle from a reference direction (). While Cartesian coordinates are written as (X, Y), polar coordinates are written as (r, ).
The graph for a polar grid differs from that for Cartesian coordinates as well. A polar grid is made up of concentric circles that radiate out from the pole.
The coordinate plane’s origin is represented by the pole. Most people use degrees or radians to map or define a polar grid.
They then note the numerous angles in that unit. The coordinates look slightly different when plotted on a polar grid.
A polar coordinate of (2, 30°) indicates that the coordinate is 2 units to the right of the origin on the r-axis with a 30-degree angle.
When employing radians, an example may be (2, (/4)). Many trigonometry problems will require students to translate from Cartesian coordinates to polar coordinates.
Students will then need to grasp how to convert between the two. If something goes wrong during the conversion, their answers will be incorrect as well.
The following is an example of converting between two distinct coordinates. To convert cos from Cartesian to polar, start by listing X and dividing it by r.
This yields the polar coordinate, which is X = r cos. It’s also useful to understand that r2 = x2 + y2.
You have to do a lot of algebra merely to have the correct functions to deal with before you can even begin to go into the nitty-gritty of trigonometry. Trigonometry is difficult due to the use of polar coordinates.
Trigonometry demands numerous distinct styles of reasoning to solve its equations. It necessitates critical and visual thinking.
Because trigonometry is related to graphs, circles, and triangles, it can aid an individual’s learning of this field of math if they are already a visual learner.
A visual learner is someone who learns topics better after seeing them. To grasp the principles, they normally require their teacher to walk them through a few distinct visual examples.
These people may find trigonometry easier to understand since they have a shorter time picturing coordinates and angles.
However, those who are not visual learners may have a more difficult time learning trigonometry.
They may take a little longer to grasp topics because they aren’t as good at visualizing.
Trigonometry is a branch of mathematics that is based on visual and critical thinking.
Those who can envision angles, triangles, and circles in their heads while conducting the math will find it easier to understand than those who cannot. Some people struggle to understand trigonometry because it is so visual.
9. Relationships Between Functions and Triangle Sides
The six functions employed in trigonometric equations are one of the first things students learn while beginning trigonometry.
Sine, cosine, and tangent all represent various triangle sides. SohCahToa is a popular nickname for the sides they represent.
The opposing length and hypotenuse length are represented by sine. The neighboring length and hypotenuse length are represented by cosine.
Tangent is the opposite and adjacent lengths. It is common for students to confuse these functions when they first begin learning trigonometry.
Sine and cosine are the easiest to confuse because they sound similar and have only one significant difference.
This becomes significantly more complicated when arc functions are added. Students will next need to recall what arcsine and arccosine mean.
If they forget and utilize the erroneous lengths, all of their subsequent math will be inaccurate.
Even if they calculate everything precisely, the final answer will be inaccurate since they utilized the improper lengths.
Because trigonometry can take a long time, that’s a lot of effort and time lost. When you first start off with trigonometry, it’s simple to utilize the wrong lengths for the functions.
10. Calculation Length
The third reason trigonometry is difficult is that solving its equations might take a lengthy time.
It also employs a variety of variables and symbols to represent the numerous functions involved in the calculation.
If the student forgets what one sign symbolizes, the rest of the calculation will be ruined.
Because of the length of time required to solve a complex trigonometric equation, there are more chances for anything to go wrong.
The more steps involved, whether it’s converting degrees to radians or radians to degrees, the more likely they’ll get an inaccurate response.
That’s because when numerous steps are required to solve a problem, the student is more likely to jot down the wrong number, skip a step by accident, or even type the wrong amount into their calculator.
With longer math tasks, small mistakes caused by human error become more likely.
When it comes to trigonometry, an extremely exact sort of arithmetic, even the smallest error might result in a completely incorrect answer.
Longer difficulties fatigue the mind much more. Students’ minds fatigue when they have to answer multiple long trigonometric equations.
This raises the possibility of inaccuracy. Trigonometry is difficult because the solutions can require multiple stages and a significant amount of time to arrive at.
Trigonometry is an ancient subject of mathematics that dates back to Ancient Greece.
Despite the fact that it has been around for a long time, understanding this form of math is still difficult.
Conversions, memorization, and reliance on visuals all contribute to the complexity of this subject of mathematics.
It is not, however, as sophisticated as calculus, which incorporates trigonometry and several other fields of mathematics. Do well to like, comment and share.