In integral calculus, the tangent half-angle substitution is a change of variables used for evaluating integrals, which converts a rational function of trigonometric functions of into an ordinary rational function of by setting . This is the one-dimensional stereographic projection of the unit circle parametrized by angle measure onto the real line. The general transformation formula is: The tangent of half an angle is important in spherical trigonometry and was sometimes known in the 17th century as the half tangent or semi-tangent. Leonhard Euler used it to evaluate the integral in his 1768 integral calculus textbook, and Adrien-Marie Legendre described the general method in 1817. The substitution is described in most integral calculus textbooks since the late 19th century, usually without any special name. It is known in Russia as the universal trigonometric substitution, and also known by variant names such as half-tangent substitution or half-angle substitution. It is sometimes misattributed as the Weierstrass substitution. Michael Spivak called it the "world's sneakiest substitution". (Wikipedia).
Tangent Half-Angle Substitution
This video describes the useful tangent half-angle substitution.
From playlist Integration Tricks
How to determine the half angle of tangent when given a triangle
π Learn how to evaluate the tangent of a half-angle. When given the value of the tangent of an angle, we can evaluate the tangent of half the angle using the tangent half-angle formula. When the value of any other trigonometric function of an angle is given, we can evaluate the tangent of
From playlist Half Angle Formulas
Evaluate the half angle of tangent from a triangle
π Learn how to evaluate the tangent of a half-angle. When given the value of the tangent of an angle, we can evaluate the tangent of half the angle using the tangent half-angle formula. When the value of any other trigonometric function of an angle is given, we can evaluate the tangent of
From playlist Half Angle Formulas
How to evaluate the half angle for the tangent function
π Learn how to evaluate the tangent of a half-angle. When given the value of the tangent of an angle, we can evaluate the tangent of half the angle using the tangent half-angle formula. When the value of any other trigonometric function of an angle is given, we can evaluate the tangent of
From playlist Half Angle Formulas
Evaluate the half angle of tangent using a triangle
π Learn how to evaluate the tangent of a half-angle. When given the value of the tangent of an angle, we can evaluate the tangent of half the angle using the tangent half-angle formula. When the value of any other trigonometric function of an angle is given, we can evaluate the tangent of
From playlist Half Angle Formulas
How to Evaluate the tangent of double angle using the tangent double-angle formula
π Learn how to evaluate the tangent of a half-angle. When given the value of the tangent of an angle, we can evaluate the tangent of half the angle using the tangent half-angle formula. When the value of any other trigonometric function of an angle is given, we can evaluate the tangent of
From playlist Half Angle Formulas
Using the half angle formula for tangent to evaluate from a triangle
π Learn how to evaluate the tangent of a half-angle. When given the value of the tangent of an angle, we can evaluate the tangent of half the angle using the tangent half-angle formula. When the value of any other trigonometric function of an angle is given, we can evaluate the tangent of
From playlist Half Angle Formulas
How to use the half angle of cosine when given a triangle
π Learn how to evaluate the tangent of a half-angle. When given the value of the tangent of an angle, we can evaluate the tangent of half the angle using the tangent half-angle formula. When the value of any other trigonometric function of an angle is given, we can evaluate the tangent of
From playlist Half Angle Formulas
Trigonometric Integrals (OpenStax Calculus, Vol. 2, Section 3.2)
This video contains solutions to sample problems from OpenStax Calculus, Volume 2, Section 3.2: Trigonometric Integrals. OpenStax Calculus Vol. 2: https://openstax.org/details/books/calculus-volume-2 Note: This is a corrected version of a previous video that contained an error in the so
From playlist Calculus II
How to Solve Trigonometric Equations (Precalculus - Trigonometry 22)
A very In-Depth look into solving equations that involve trig functions. We will focus on solving equations without having to use inverse trigonometric functions and relating solutions to the unit circle. Support: https://www.patreon.com/ProfessorLeonard
From playlist Precalculus - College Algebra/Trigonometry
Learn to evaluate the half angle for cosine
π Learn how to evaluate the tangent of a half-angle. When given the value of the tangent of an angle, we can evaluate the tangent of half the angle using the tangent half-angle formula. When the value of any other trigonometric function of an angle is given, we can evaluate the tangent of
From playlist Half Angle Formulas
Trigonometric Substitution (OpenStax Calculus, Vol. 2, Section 3.3)
This video contains solutions to sample problems from OpenStax Calculus, Volume 2, Section 3.3: Trigonometric Substitution. OpenStax Calculus Vol. 2: https://openstax.org/details/books/calculus-volume-2
From playlist Calculus II
Math 031 Spring 2018 020718 Trigonometric Substitution
Method of trigonometric substitution: use the Pythagorean identities. Examples of trigonometric substitution.
From playlist Course 3: Calculus II (Spring 2018)
Sum and Difference Compound Identities 2 Adv Examples
I work through 2 fun problems involving sum and difference identities and double angle identities in trigonometry, otherwise known as compound angle identities. Check out http://www.ProfRobBob.com, there you will find my lessons organized by chapters within each subject. If you'd like to
From playlist IB Higher Level Mathematics
How to Use the Double and Half Angle Formulas for Trigonometry (Precalculus - Trigonometry 28)
LOTS of examples of using the Double Angle and Half Angle formulas in Trigonometry. Support: https://www.patreon.com/ProfessorLeonard
From playlist Precalculus - College Algebra/Trigonometry
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From playlist Precalculus - College Algebra/Trigonometry
This popular problem is stumping everyone, and many, many people emailed it to me. I give extra thanks Chaitanya from India who was the first person who sent it to me. I also thank David K, Achille Hui, and Seyed who found geometric solutions to this problem when I posted it to Math Stack
From playlist Math Puzzles, Riddles And Brain Teasers
Evaluate the half angle for cosine from a triangle
π Learn how to evaluate the tangent of a half-angle. When given the value of the tangent of an angle, we can evaluate the tangent of half the angle using the tangent half-angle formula. When the value of any other trigonometric function of an angle is given, we can evaluate the tangent of
From playlist Half Angle Formulas