Skip to main content

The Inverse & Reciprocal TRIGONOMETRIC Functions

So, this is my second post on trigonometry. In this post we're gonna cover the reciprocal and the inverse Trigonometric functions. If you haven't seen my first post you should definitely view it as it covers the basics of Trigonometry

The Reciprocal Trigonometric Functions

The reciprocal Trigonometric function of Sine is Cosecant, of Cosine is Secant & for Tangent it is Cotangent.
  • Cosecant (Csc θ = 1/Sin θ) or (Hypotenuse/Opposite)
  • Secant (Sec θ = 1/Cos θ) or (Hypotenuse/Adjacent)
  • Cotangent (Cot θ = 1/Tan θ) or (Adjacent/Opposite)
We can also represent Tan θ in another way. As Tan θ = opposite/adjacent
 & Sin θ = opposite/hypotenuse
 & Cos θ = adjacent/hypotenuse
∴ Tan θ = Sin θ/Cos θ (The hypotenuses cancel out)
As Cot θ = 1/Tan θ 
So, we can also represent Cot θ as Cos θ/Sin θ.



The Inverse Trigonometric Functions

In trigonometry the inverse trigonometric functions sin-1 , cos-1, tan-1, csc-1, sec-1, cot-1 (aka cyclometric functions) are the inverse functions of sin, cos, tan, csc, sec, cot respectively.
This means that the sin-1  of a value, say x would be the angle which gives x when its sine is taken
If you cant understand this, I'll give some examples which would make you understand the concept

sin-1 (1/2) = ? (This means that which angle when taken the sin of, gives the value as 1/2)
So, sin-1 (1/2) =30° (sin 30 = 1/2)

Example

Heres an example that can make you see the use of the inverse trigonometric functions

There's an alien standing on the top of Burj khalifa (828 meters), and there's a MIB agent standing on the roof of another building 8 meters long and the distance between the base of the burj khalifa and the building where the agent is standing is 100 meters. Find the angle at which the agent should shoot his Ray gun to vaporize the alien. Round off your answer to the nearest hundredths.


Solution - Lets first construct the triangle which joins the agent, the alien and the point 8m above the base of Burj khalifa. Lets label the required angle as θ
The opposite side to theta will be 820 m (total height of building - the height at which the agent is standing)
We know 2 sides - The adjacent and the opposite
Which trigonometric function deals with opposite and adjacent? Well, we know that Tan θ = opp/adj
∴ Tan θ = 820/100
   Tan θ = 82/10 = 41/5 = 8.2
   Tan-1(Tan θ) = θ
⇒Tan-1(8.2) = θ
use calculator to figure Tan-1(8.2) ,
θ = 83.0470425°
θ ≈ 83.05°
So, the agent has to shoot his gun roughly at an angle of 83.05° to hit the alien

 I hope you liked the post, if you have any doubt, leave it in the comments section below.
In the next post we will move on to trigonometry with general triangles and also some special right triangles.
Stay tuned for more :D




You may also like:

High School Pedia- www.highschoolpedia.com
Labels:

Comments

  1. Math on Rough Sheets17 August 2019 at 22:26

    Very informative article, Which you have shared here about the Inverse & Reciprocal Trigonometric functions. After reading your article I got very much information and it is very useful for us. Mathinstructor is the best platform where you can Find Y Intercept Of Quadratic Functions online.

    ReplyDelete
  2. fgfgf13 November 2022 at 21:36

    1833 S Coast Hwy, Oceanside, CA, 92054 is the beauty salon in Oceanside, CA where you can take advantage of a huge range of services and forget about your worries at least for a little bit. We now have over 15 years of experience and this is just one of the reasons why we are able to provide you with so many amazing services. But if you are still not sure whether to set an appointment with us, you should read the following paragraphs and learn a bit more about us.

    Why Are We Different?

    nail salons near oceanside ca

    At our nail and spa salon Oceanside CA, you can treat yourself to a nice manicure and pedicure, eyelash extensions, brow threading, and more. We are ready to serve each and every one of you.
    We are working only with quality products and equipment, which is the reason why everyone who takes advantage of our services will enjoy long-lasting and beautiful results.
    If you found us online, you can take advantage of a 10% discount on the first procedure you get at our salon.
    Our extensive experience in the beauty industry is the reason why so many people choose our beauty salon. We can meet all your requirements and will answer any questions you may have.

    If you are currently looking for a nail and spa salon in Oceanside, CA, you should try 1833 S Coast Hwy, Oceanside, CA, 92054 and all the amazing services we offer! Stop by the salon if you have questions or want to set up an appointment, or just give us a call at (760) 721-4876 right away!

    ReplyDelete

Post a Comment

Popular Posts

High School Pedia

It is an initiative by some students to spread the light of knowledge to everyone and everywhere. It was started in the year 2015 and has grown rapidly in the past few months. By the means of this website, we try to provide information on every topic that we can reach up to. You can find different articles on this website. All these articles are written in simple language so that everyone can understand it and learn from it. We at High School Pedia believe in creative learning and this is the reason why we add our own edited graphical representations in every article. Once a very learned man said, “Knowledge increases by not keeping it to yourself but by sharing it with others”. And we follow the same motto “Share to Learn”. The team of High School Pedia tries its best to provide you with the best and original content. Unlike many other websites, High School Pedia is famous for its original and inspiring content.
2 comments
Read more

Animal and Plant Cells

 Cells Cells are the basic functional, biological and structural unit of life. The word cell is a Latin word meaning ‘small room’. Cells are also known as building blocks of life.  The branch of science that deals with the form, structure, and composition of a cell is known as Cytology. All organisms around us are made up of cells. Bacteria, ameba, paramecium, algae, fungi, plants and animals are made up of cells.  Cells together form tissues. And tissue together makes an organ. History Of Cell The cell was discovered by Robert Hooke in 1665. He assembled a simple microscope and observed a very thin slice of cork under his primitive microscope. The cork was obtained from the outer covering of a tree called bark. Robert Hooke observed many little-partitioned boxes or compartments in the cork slice. These boxes appeared like a honey-comb. He termed these boxes as the cell. He also noticed that one box was separated from another by a wa...
23 comments
Read more

Permutation and Combination

Permutation and Combination Hey guys, I am back with one more interesting mathematics topic. And I am pretty sure that you guys would find it interesting too because many of you must have faced problems regarding these arrangements. Although if you were not able to solve them at that moment of time I am sure after completing this article you would solve the problem in minutes or even seconds. WHAT IS THE DIFFERENCE ?? Many people get confused between these two terms permutation and combination. They both have almost similar use but have a vast difference in their meaning. You may think that both of them mean arranging entities, then what is the difference ?? For making it easy we will take an example, lets say I have four friends : Arya, Bhavesh, Chirayu and Dhruv. So if I arrange them like Arya, Bhavesh, Chirayu and Dhruv or Dhruv, Chirayu, Bhavesh and Arya, it will make no difference in combinations but if you check them according to permutation they will be different. As ...
5 comments
Read more

Levitation 2

LEVITATION II To be completely honest I was going to start this with a pun. I did think of one but it doesn’t float… I am sorry I just had to. Anyway, this is the second part to the article on super cool ways of making things levitate. Go check the first part out if you haven’t already. Actually, the first part may have become repulsive with all the magnets and stuff, but I promise this will be more attractive. Get it? No? I’ll stop now. I am just going to jump straight into it. 1.    Electrostatic Levitation I know you are probably sick and tired of magnets but they are the best way you know… This method is somewhat similar. You remember that cool science experiment you did with two straws attracting or repulsing each other based on their charge? So basically using the same principle we can make a charged object levitate. But before you try it, let me tell you it won’t be easy. Even impossible according to our Mr. Earnshaw. He even made a law (th...
4 comments
Read more

Catalysts

Catalysts When we hear the word catalyst, the first thing that comes to mind is the game “Mirror’s Edge Catalyst”. But actually, catalysts are chemical substances that speed up the process of a chemical reaction but do not used up in the process of speeding up. The process of using catalysts to speed up chemical processes is called catalysis. Some examples are: Ø Hydrogen peroxide decomposes to form water and oxygen. 2H2O2 à 2H2O + O2 But in the presence of manganese dioxide (MnO2) the process is sped up and happens a lot faster. Ø Cars use a catalytic converter to convert carbon monoxide to carbon dioxide. These contain Platinum to speed up the process and keep the car’s system getting backed up. Ø Ammonia synthesis also uses Iron as a catalyst Catalysts work by reacting with a reactant. This is called a catalytic action. The product of the catalytic action is a chemical intermediate, which can react with the other reactant at a faster pace and give...
Post a Comment
Read more

Animals Known for Their Colours...

We all love colours, don't we? Listed down below are the Animals known for their colours and beauty:- 1) Mandarin Fish        The mandarin fish is a saltwater fish found in the Pacific Ocean. It sports a bright blue background, with swirly orange stripes and a blue-greenish face. Its attractive colours are due cellular pigmentation. They are usually reef dwellers. 2) Pheasant Pheasants are mainly found in Central Asia and Western Europe. The male bird has colourful feathers and an attractive long tail. Their colour varies between golden, brown, green, white and purple. While the head of male pheasants are red in colour, female pheasants are paler in this aspect.
Post a Comment
Read more