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

Android Versions Named After Sweet

Have you ever thought why are Android versions always named after sweet names ?? Everytime a new Android version is launched its name is kept after a sweet name. Many people have researched about this topic and many have asked Google also. Have you ever tried to find out the core reason behind this? If not then you would find the answer here . First of all let us first see what Google says about this : In 2008 i.e. the year when Android was launched a reporter asked the reason for the same. At that time Google said “It’s kind of like an internal team thing, and we prefer to be a little bit — how should I say — a bit inscrutable in the matter, I’ll say,” said Randall Sarafa, a Google spokesman. “The obvious thing is that, yeah, the Android platform releases, they go by dessert names and by alphabetical order for the most part."
15 comments
Read more

2-D & 3-D GEOMETRY

2-D & 3-D GEOMETRY We all have some amount of geometry. We know that any line can be represented on the Cartesian plane. Any figure can be drawn on it. But can we represent a 3-d object on it. Yes we can. A Cartesian plane has 2 axis. While representing in 3-D we need to add a third axis. This axis does not come in between the axis or in the same plane. It appears to be coming out of the paper as we cannot represent a 3-d object on a 2-d surface. This new z-axis represents a line coming out of the screen. Before understanding 3-d geometry you need to imagine this axis coming out of the screen.  REMEMBER : all the three axis are perpendicular .i.e there an angle 0f 90 between them and they meet at the origin If you are unable to imagine you can take a thick book as an example. Any corner becomes it origin and the three edges as the three axis REPRESENTING 3-D GEOMETRY Like in 2-d geometry we represent the value of the different axis as (x,y) we use the sa...
3 comments
Read more

Finding Square Roots Easily (Vedic Math)

Finding Square Roots Easily (Vedic Math) Hello, Guys!!! I’m back with another post on Vedic Math that is going to keep you glued rooted to your spot 😆. This time I’m going to teach you how to calculate the square roots of perfect squares faster… With a little practice, this method can let you calculate the roots in a matter of 5 seconds, whereas if you had used the traditional method, you would still be stuck with your question 😏 Things you need to know:- Perfect square which has unit digit 1 will have square root with the last digit as 1 or 9 Perfect square which has unit digit 4 will have square root with the last digit as 2 or 8 Perfect square which has unit digit 5 will have square root with the last digit as 5 Perfect square which has unit digit 6 will have square root with the last digit as 4 or 6 Perfect square which has unit digit 9 will have square root with the last digit as 3 or 7 Perfect square which has unit digit 0 will have square r...
Post a Comment
Read more

AxonVR

Hey, guys ! Everybody's talking about virtual reality these days, but I bet you haven't imagined how real it is getting. The AxonVR is landing in the world of technology and I am pretty sure that a new era of technology begins from here!
Post a Comment
Read more

UEFA CHAMPIONS LEAGUE

UEFA CHAMPIONS LEAGUE Europe's biggest club soccer competition, The UEFA Champions League, takes place every year. The competition begins in September and ends in May. It is a classic tournament following a round-robin format after which the top teams qualify to the knockout stages. It includes 32 best clubs in different countries of Europe. Obviously teams from major countries like England, Spain, France, Germany and Italy qualify easily while teams from smaller countries like Ireland, Austria, Netherlands, Denmark have to go through a qualifying round. The teams who win the leagues in their countries qualify directly while in some countries even the second, third and fourth placed teams also qualify. Sometimes a team may qualify in the Champions League because they finished in the top-four. These clubs may or may not qualify through their leagues but their good performance may help them qualify. Even the champions of The UEFA Europa League, another prestigious league ...
Post a Comment
Read more