# Inverse Trigonometric Functions and their Applications

### Please Discuss about inverse trigonometric functions based on a practical example from everyday life. (STEM applications).

Bring the example and show how the inverse functions apply to solve the problem.

## 23 thoughts on “Inverse Trigonometric Functions and their Applications”

1. Khadra Shihadeh says:

One example of an inverse trigonometric function is the angle of depression and angle of elevation. I believe these two fit as a plausible example because they use sine or cosine or tangent in order to determine the angle of a persons view to the top of a building for example. Or another example would be if a person is standing on a building that is a certain height and looking down at a object a certain distance away, what would be the angle of depression that they’re looking down. That example I believe uses more of the inverse aspect of trigonometric functions as you would set up all the variables and solve for the angle. As stated, in other instances you could have a height and a degree value and solve for the variable missing like distance. These are some examples of what comes to mind for me when I hear the phrase trigonometric inverse functions because it is both that and furthermore something to use in the real world.

2. Anthony Leung says:

An example of people using inverse trigonometric functions would be builders such as construction workers, architects, and many others. An example of the use would be the creation of bike ramp. You will have to find the height and the length. Then find the angle by using the inverse of sine. Put the length over the height to find the angle. Architects would have to calculate the angle of a bridge and the supports when drawing outlines. These calculations are then applied to find the safest angle. The workers would then uses these calculations to build the bridge.

3. Kennethm says:

One use of inverse trigonometric functions in real life is if for example say you are a carpenter and you want to make sure that the end of a piece of wood molding is cut at a 45-degree angle. You can measure the side lengths at the end of the molding and use an inverse trigonometric function to determine the angle of the cut. Therefore inverse trig functions can be used for other functions related to carpentry like construction etc.

4. jose rodriguez says:

An example of the use of inverse trigonometric functions in the real world is Carpentry. So during carpentry work angles are made all the time to make sure the material and other equipment can fit exactly in the space that is available. one example in carpentry is making 45 degree angles onto molds so it can turn corners. so to make a 45 degree angle you would need to imagine a right triangle on the thinnest part of the mold and you would need to find out the measurement of the adjacent and opposite sides, after you use TAN to find the hypotenuse so you accurately find the measurement you need to cut to get a perfect 45 degree angle cut.

5. Michael Colon says:

Inverse trigonometric functions are commonly used in engineering, construction, and architecture. For example, archeologists discovered an ancient ruin on the peak of a steep mountain. They have heavy machinery, however, they cannot bring it up a steep slope. They can find the elevation of the paths in order to determine the best route for the machinery to take. If the route ends 200ft above their current position, 400ft horizontal and the machinery cant go at a greater angle than 40 degrees, they can use inverse trig functions to find the angle of the route. Based on their findings, they can find the best route to take up the mountain.

6. steve vargas says:

We can view a function as something that maps things of one type to things of another type. The inverse of a function tells you how to get back to the original value. We do this a lot in everyday life, without really thinking about it. For example, think of a sports team. Each player has a name and a number. So if you knew a players name and wanted to know their number, you could think of this as a function from players to their numbers. Now, if you wanted to do the reverse, find a players name given their number, you would be using the inverse of this function. Another example: suppose I am travelling at 60 miles per hour, and want to know how far I have gone in x hours. Then this could be represented by the function(x) = 60 * x Now I want to know the inverse: If I know I have traveled x miles how long have I been travelling for? f^{-1}(x) = x/60

7. Abhijeet says:

One example on how inverse functions are used in real life are currencies. If you would want your money to be converted to another type of currency, For example if you have U.S dollars and you want to convert it into pesos you would have to use a function to convert it and if you would want to convert it back to u.s dollars you would have to use the inverse functions. If I were to convert 1 US dollar to pesos it would be 18.97 and to find out if this is true I would have to use a function. Which would be y=x-18.97 where y is the amount of pesos and x is how many US dollars you are trying to convert. With this formula we can find out the amount of pesos equivalent to the dollars we are trying to convert inputted. If we were to convert the pesos back to US dollars we would have to use the inverse function y=x/18.97 in order to get the original amount back. Y represents the amount of dollars and x represents the pesos.

8. Norbert Sziffer says:

Inverse functions are used in physics, astronomy, navigation, construction and in many other fields. They are often used in every day life. For example if someone is mapping out hiking trip. On your map, you know that you supposed go on the course that ends with you having to move 2.5 miles east and 3 miles south. And now we have to calculate the angle that you need to walk with respect to due East. We can set up a triangle that matches the physical situation of this problem. In this case we use arctan to find the angle.

9. Lucie Mingla says:

Thank you for bringing such great examples of using inverse functions in STEM applications. I truly value your input.

10. Lucie Mingla says:

Thank you for bringing such great examples of using inverse functions in STEM applications. I truly value your input.

11. Andrew Gardner says:

One way I can explain about inverse functions is through national currency where a person can measure their currency in value to another region. For example, you’re in the United States who want to visit Germany on vacation and you want to exchange some money into euros and euros are currently valued at $1.12 dollars in the United States. The function for Germany value would be y=$1.12X. Let Germany =Y and US = x and y=1. y = ax. Y =$1.12x => Y/1.12 = X => 1/1.12 = x => X =$0.98. This would be the value of Germany currency to United States currency. The inverse function of this which is F^-1(0.98), Let US Currency= X, Germany currency = y and x=1. X = 0.98Y => x/0.98 =y => 1/0.98= y => \$1.12 = Y. This shows that you can measure your currency for any country with the use of the inverse function and get back the same value which is a one to one function.

12. tshorma says:

Inverse sign are very important and fundamental in the world we live and how we interact. Inverse trigonometric functions like such sin^(−1) (x) , cos^(−1) (x) , and tan^(−1) (x) , are used to find the unknown measure of an angle of a right triangle, and can also be used when there is a missing side. You can also use To calculate other objects not just triangle. During my experience take EMT 1220, my professor used the inverse sin function to find the radius of the sun. Its a very helpful fundamental law to understand in geometry and most certainty in trig

13. tshorma says:

Inverse sign are very important and fundamental in the world we live and how we interact. Inverse trigonometric functions like such sin^(−1) (x) , cos^(−1) (x) , and tan^(−1) (x) , are used to find the unknown measure of an angle of a right triangle, and can also be used when there is a missing side. You can also use To calculate other objects not just triangle. During my experience take EMT 1220, my professor used the inverse sin function to find the radius of the sun. Its a very helpful fundamental law to understand in geometry and most certainty in trig

14. tshorma says:

Inverse sign are very important and fundamental in the world we live and how we interact. Inverse trigonometric functions like such sin^(−1) (x) , cos^(−1) (x) , and tan^(−1) (x) , are used to find the unknown measure of an angle of a right triangle, and can also be used when there is a missing side. You can also use To calculate other objects not just triangle. During my experience take EMT 1220, my professor used the inverse sin function to find the radius of the sun. Its a very helpful fundamental law to understand in geometry and most certainty in trig

15. tshorma says:

Inverse sign are very important and fundamental in the world we live and how we interact. Inverse trigonometric functions like such sin^(−1) (x) , cos^(−1) (x) , and tan^(−1) (x) , are used to find the unknown measure of an angle of a right triangle, and can also be used when there is a missing side. You can also use To calculate other objects not just triangle. During my experience take EMT 1220, my professor used the inverse sin function to find the radius of the sun. Its a very helpful fundamental law to understand in geometry and most certainty in trig

16. Adrian Guin says:

Inverse Trigonometric Functions can be very useful in the real world and not just in math class. An example can be in aviation, if two aircraft depart from an air base at the same speed forming an angle and following straight paths, you can determine the distance between them. Or In the ocean a captain of a ship can determine the wrong course of the ship, always in a straight line, ordering to modify the course in the degree to go directly to the correct destination point. Using this functions: sin^(−1) (x) , cos^(−1) (x) , and tan^(−1) (x) to determine the direction they want to go.

17. Chadel says:

An examples a real life inverse function is a sports team. Each player has a name and a number. So if you knew a players name and wanted to know their number, you could think of this as a function from players to their numbers. Now, if you wanted to do the reverse, find a players name given their number, you would be using the inverse of this function.

18. Chadel says:

An examples a real life inverse function is a sports team. Each player has a name and a number. So if you knew a players name and wanted to know their number, you could think of this as a function from players to their numbers. Now, if you wanted to do the reverse, find a players name given their number, you would be using the inverse of this function.

19. Sadman Arefin says:

The inverse trigonometric function is a very important mathematical concept and can play a significant role in our everyday lives.
Application:
A person is looking at a building that’s 75ft far horizontally. The building is 60ft tall in height. We have to find the angle of elevation….
Now, we form a right triangle. We already know that the horizontal distance between the person and the building is 75ft, which is the adjacent side to the angle we are solving for. Then, the height of the building is 60ft, which is the opposite side to the angle that we are solving for. Since we have the value of the opposite side and the adjacent side of the right triangle, we can now set up a inverse tangent function to solve for the angle of elevation. Tan^-1(60/75)=38.66 degrees. So the angle of elevation is 38.66 degrees.

20. Eamon Bolger says:

For the everyday life practical example I used determining the height of a building based off its angle and the distance the person was from the building. Writing this problem out would give you a right triangle in which you could use tan to determine the height since you have the angle in our case 60 degrees and a set distance from the building which was 23 meters. we would right this out as tan60=AB/23 with the unknown variable being the height of the building. By using the unit circle you can determine that tan60=sqrt3 and you can get AB by itself by multiplying 23 on both sides. This will give you a final answer that the building is 39.84m tall. Checking the answer is where the inverse function comes into play as you can use the formula tan-1(y/x) to get 60 degrees which is the angle you were at in the beginning of the question.

21. Eamon Bolger says:

For the everyday life practical example I used determining the height of a building based off its angle and the distance the person was from the building. Writing this problem out would give you a right triangle in which you could use tan to determine the height since you have the angle in our case 60 degrees and a set distance from the building which was 23 meters. we would right this out as tan60=AB/23 with the unknown variable being the height of the building. By using the unit circle you can determine that tan60=sqrt3 and you can get AB by itself by multiplying 23 on both sides. This will give you a final answer that the building is 39.84m tall. Checking the answer is where the inverse function comes into play as you can use the formula tan-1(y/x) to get 60 degrees which is the angle you were at in the beginning of the question.

22. ChadLam says:

The inverse function could be used in our everyday life. It could be used to help us determine the height of things for instance a building.
For my project I had to determine the height of the building the bird was on as Juan wanted to caption how high the bird was. Using the angle and the distance he was away from the building I was able to determine how high the bird was. The angle was 60 degrees and I used the unit circle which told me that tan 60 degrees is sqrt(3). To find the height of the building I did tan 60 degrees = opposite/ adjacent. Which is sqrt(3) = Ab/23 to get rid of the 23 I multiplied both sides by 23 to get Ab. The height of the building was 39.84 meters tall. I used inverse function to check my work. Which is arc-tan(y/x) which is arc-tan(39.94/23) this will give me 60 degrees. This means that the building is 39.84 meters tall.

23. Brianna Persaud says:

The use of inverse functions are used in everyday life. One possibility of using this would to be while hiking. While planning the trip, you mark down that you are supposed to go on a trail which ends with you having to move 2.5 miles east and 3 miles south. You must find the angle you need to walk to east using inverse trig function. In order to do this, you find the inverse of tan (3/-2.5) which gives you an angle of -50.19