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




Comments

  1. 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. 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

Piezoelectric Crystal

Piezoelectric Crystal {literally_pressing electricity} Ever wondered what it might be like to live in dark or sleep in a hot summer day without an AC ? Absurd, isn't it ? But with the rate at which we are using our resources, it may not be long before it actually happens. Scientist across the globe are searching for new resources, stocks and technology to prevent the near, unpleasant future of current and the next gen. One of these, an unexploited tech is that of Piezoelectricity. Piezoelectricity is an ability of some special materials (like crystals of quartz, ceramics of lithium niobite, gallium arsenide, zinc oxide) to trigger an electric charge when supposed to mechanical stress. These materials are available in basic instruments that we use in our daily life like microphones, quartz watch, gramophones. All these materials are run by the piezoelectric current. But how does it work? When you apply force (mechanical force) on it, an electric potential, on eit

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.

Anode Ray Experiment

→Anode ray experiment was conducted by E Goldstein. →These rays are also known as canal rays. →This experiment helped in the discovery of the proton. Apparatus Used A discharge tube  was taken in which there were 2 electrodes i.e. Anode(+ve) and the cathode (-ve). The tube was filled with an inert gas. A perforated or porous cathode was used. A layer of zinc sulphide was placed at the back of the cathode. There was a vacuum pump in the tube. High voltage (5000v-10000v) was allowed to flow through the system. It was observed that when the gas was at 1atm(atmospheric pressure ) no change was seen in the tube.  When the   pressure   was decreased inside the tube, a glow could be seen at the back side of the cathode.

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 (the law is

Isotopes, Isobars and Isotones

Isotopes These are elements which have the same atomic number but different atomic mass . They have the same atomic number because the number of protons that are inside their nuclei remains the same. But, they have different atomic mass because the number of neutrons that are also inside their nuclei is different. As the number of protons inside nuclei remains same, therefore the overall charge of the elements also remains same as in isotopes: no of protons = no of electrons . Hence, as isotopes overall charge remains neutral, therefore their chemical properties will also remain identical.   Therefore, Isotopes are chemically same but physically different.

Upcoming Marvel Movies

Hey, guys! Today we are going to talk about the 5 most awaited and upcoming marvel movies. Everyone is eagerly waiting right ?!            1) GUARDIANS OF THE GALAXY vol.2 (2017) Last month marvel shared the first teaser of Guardians of the Galaxy vol. 2   describing it as the official sneak-peak. All five main characters- star lord, gamora, rocket, Drax and 'baby' groot . It is set two months after the first movie where the ravagers find out that peter quill double crossed them about the infinity stone (orb). That's all. Everything else is yet to be discovered.