country
$20 Bonus + 25% OFF
Securing Higher Grades Costing Your Pocket? Book Your Assignment at The Lowest Price Now!
Add File

Error goes here

Pythagorean Identities In Trigonometry

Referencing Styles : APA | Pages : 1

Three Pythagorean Identities in Trigonometry

In math, an identity is an equation which remains always true. This can be trivially true like x = x or usefully true such as the Pythagorean Theorems a2 + b2 = c2   for right angled triangles.  There are loads of trigonometric identities.  Trigonometric Identities are equations that are true for any right angled triangles.  The Pythagorean Identities in trigonometry are defined as three different identities that   come from the Pythagorean Theorem. The Pythagorean Theorem states that the hypotenuse squared of a right angled triangle is equal to the sum of the square of each   of the other two sides or a squared plus b squared. In Pythagorean Theorem, c stands for the hypotenuse and a   and b stands for the other two sides of the right angled triangle. Fromm this theorem the three identities can be determined from substituting in sine and cosine.

The first Pythagorean identity in Trigonometry:

The first identity probably looks like the Pythagorean theorem.

 

This identity of Pythagorean Theorem comes from the unit circle. All the right angled triangles formed by this unit circle will have their hypotenuse as 1. With the hypotenuse of 1 and an angle at the origin of the coordinate plane on which the circle is drawn, the relationship between the sides and the sine and cosines can be formed.  This identity is useful when a problem is seen with a sine squared plus a cosine squared. One can use this identity and replace the sine squared plus the cos squared with the 1.

The Second Pythagorean Identity in Trigonometry:

The second identity that comes from the first has one of the sides equal to 1. In order to arrive at this identity, the first identity is divided by the sine squared so as to get the other side equal to 1. I t is known that cosine squared divided by sine squared is cotangent squared and also 1 divided by the sine squared is cosecant squared.

 

The Third Pythagorean Identity in Trigonometry:

The third Pythagorean identity that can be arrived by dividing both sides by cos2(θ) in order to get the identity

1 + tan2(θ) = sec2(θ)

The Pythagorean identities are very useful for simplifying the complicated trig statements and equations.

Example 1: Use Pythagorean Identities in order to find the missing trigonometric values.



find the value of the other trig functions

The easiest Pythagorean Identity to work with is 
sin2θ +cos2θ = 1. 

 

 

 

 

 

 

 

Example 2:

Use Pythagorean Identities to help simplify trig expressions.

 

 

Simplify:    sinx cos2x - sinx

 

 

 

Since this expression contains sine and cosine, utilize sin2θ +cos2θ = 1 or its variations.
Start by factoring:

 

 

Example 3:

Use Pythagorean Identities to help simplify a trig expression into a factorable form.

 

 

Express csc2x - cotx - 3 in factored form.

 

 


Start by substituting:

 

 

 

 

Example 4:

If \sin(30^\circ) = \frac{1}{2},sin(30∘)=21​, what is \cos(30^\circ)?cos(30∘)?

By the Pythagorean identity,

sin2(30∘)+cos2(30∘)=1

Hence,

cos2(30∘) = ±3/2

Example 5:

Simplify  using the Pythagorean identities



This is good, but we can go even further. If  then we can rearrange this identity by moving the 1 to the other side:  and then multiplying both sides by -1:  . Thus, our expression actually equals:




Being able to manipulate expressions will be helpful when solving more complex equations.

Example 6:

Example 7:

Deriving the Pythagorean identities lead to the understanding of the basic trigonometric proofs. Doing so will help them in solving an equation in both sides of the equation which can be manipulated to find a solution. However while proving for an identity; only one side of the identity can be manipulated. Pythagorean identities can be used for rewriting the trigonometric equations in equivalent form.

The Pythagorean Theorem allows an individual to convert between the sine and cosine values of an angle without being aware of the angle itself. Considering the example, the angle θ in quadrant IV for which the sin(θ) = -24/25. Here the Pythogorean identity can be used along with sin(θ) , in order to solve for cos(θ) .

While solving it the required answer would be cos(θ) = 7/25.

Thus Pythagorean identities can be used to simplify trigonometric expressions in terms of writing other trigonometric functions.

Solutions

OR

MyAssignmenthelp.com offers best thesis writing service in USA. We offer the right platform for those who often search can anyone help me write a thesis perfectly. With a pool of qualified and experienced online thesis makers, we provide highest quality PHD thesis writing services to students in USA. Our PhD thesis help services include writing help, help with selecting topics, assistance for researching and editing and proofreading help.

Save Time & improve Grade

Just share requirement and get customized Solution.

watch
question
We will use e-mail only for:

arrow Communication regarding your orders

arrow To send you invoices, and other billing info

arrow To provide you with information of offers and other benefits

Add File

Error goes here

1,544,311

Orders

4.9/5

Overall Rating

5,108

Experts

Our Amazing Features

delivery

On Time Delivery

Our writers make sure that all orders are submitted, prior to the deadline.

work

Plagiarism Free Work

Using reliable plagiarism detection software, Turnitin.com.We only provide customized 100 percent original papers.

time

24 X 7 Live Help

Feel free to contact our assignment writing services any time via phone, email or live chat. If you are unable to calculate word count online, ask our customer executives.

subject

Services For All Subjects

Our writers can provide you professional writing assistance on any subject at any level.

price

Best Price Guarantee

Our best price guarantee ensures that the features we offer cannot be matched by any of the competitors.

Our Experts

Assignment writing guide
student rating student rating student rating student rating student rating 5/5

1896 Order Completed

95% Response Time

Herman Berens

MSc in Psychology

London, United Kingdom

Hire Me
Assignment writing guide
student rating student rating student rating student rating student rating 5/5

647 Order Completed

98% Response Time

Adlina Han

Masters in Marketing with Specialization in Branding

Singapore, Singapore

Hire Me
Assignment writing guide
student rating student rating student rating student rating student rating 4/5

3076 Order Completed

99% Response Time

Emily Wei

Doctor of Philosophy (Ph.D) in Civil Engineering

Singapore, Singapore

Hire Me
Assignment writing guide
student rating student rating student rating student rating student rating 5/5

1692 Order Completed

98% Response Time

Alfred Dodd

PhD in Computer and Information Science with specialization in Database

Wellington, New Zealand

Hire Me

FREE Tools

plagiarism

Plagiarism Checker

Get all your documents checked for plagiarism or duplicacy with us.

essay

Essay Typer

Get different kinds of essays typed in minutes with clicks.

edit

GPA Calculator

Calculate your semester grades and cumulative GPa with our GPA Calculator.

referencing

Chemical Equation Balancer

Balance any chemical equation in minutes just by entering the formula.

calculator

Word Counter & Page Calculator

Calculate the number of words and number of pages of all your academic documents.

Refer Just 5 Friends to Earn More than $2000

Check your estimated earning as per your ability

1

1

1

Your Approx Earning

Live Review

Our Mission Client Satisfaction

Thank you, thank you, thank you. i already get A for this subject because i'm using my assigment help. actually it really helping me so much. My lecture has been proud of me. Thank you to expert team from assigment help they are really friendly, they...

flag

User Id: 449623 - 16 Jan 2021

Australia

student rating student rating student rating student rating student rating

My instructor was quite impress. However, there were too many grammatical errors present especial spelling please remember that certain words are spelt differently in the USA.

flag

User Id: 400095 - 16 Jan 2021

Australia

student rating student rating student rating student rating student rating

the expert he do his best in this assignment and he delivered to me in the time and I get high marks. i appreciate the expert who work for me on this assignment

flag

User Id: 124147 - 16 Jan 2021

Australia

student rating student rating student rating student rating student rating

I appreciated his work I will recommend this site to all my friends. the expert he do his best in this assignment and he delivered to me in the time and I get high marks,

flag

User Id: 124147 - 16 Jan 2021

Australia

student rating student rating student rating student rating student rating
Pythagorean Identities In Trig... has been added in your library.
callback request mobile
Have any Query?