INTEGRAL OF TRIGONOMETRIC FUNCTIONS After completing this topic, you - PowerPoint PPT Presentation

Oct 08, 2022 •17 likes •67 views

SUBJECT:MATHEMATICS LEVEL: 4 TOPIC 2: FUNCTIONS AND ALGEBRA INTEGRAL OF TRIGONOMETRIC FUNCTIONS After completing this topic, you will be able to: Find the indefinite integral of different trigonometric functions TSC-0-06-6992-2020-R00

SUBJECT:MATHEMATICS LEVEL: 4 TOPIC 2: FUNCTIONS AND ALGEBRA
INTEGRAL OF TRIGONOMETRIC FUNCTIONS After completing this topic, you will be able to: • Find the indefinite integral of different trigonometric functions TSC-0-06-6992-2020-R00 MATHEMATICS LEVEL 4 2020-06-30 DPA/mlm Page 2
INTEGRAL OF TRIGONOMETRIC FUNCTIONS. • Lets find the integral of the form 𝑡𝑗𝑜 𝑙𝑦 𝑒𝑦 = −𝑑𝑝𝑡𝑙𝑦 + 𝑑 find 1) 𝑡𝑗𝑜6𝑦 𝑒𝑦 • = −𝑑𝑝𝑡6𝑦 + 𝑑 6 2) 3𝑡𝑗𝑜4𝑦 𝑒𝑦 • = 3 𝑡𝑗𝑜4𝑦 𝑒𝑦 • = −3𝑑𝑝𝑡4𝑦 + 𝑑 4 TSC-0-06-6992-2020-R00 MATHEMATICS LEVEL 4 2020-06-30 DPA/mlm Page 3
INTEGRAL OF TRIGONOMETRIC FUNCTIONS. • Lets find the integral of the form 𝑑𝑝𝑡 𝑙𝑦 𝑒𝑦 = 𝑡𝑗𝑜𝑙𝑦 + 𝑑 • Find 𝑑𝑝𝑡2𝑦 𝑒𝑦 • = 𝑡𝑗𝑜2𝑦 + 𝑑 2 • 3𝑑𝑝𝑡3𝑦 𝑒𝑦 • = 𝑑𝑝𝑡3𝑦 + 𝑑 TSC-0-06-6992-2020-R00 MATHEMATICS LEVEL 4 2020-06-30 DPA/mlm Page 4
ACTIVITY • FIND a) 3cosx + 2sin2x dx b) 2sin3x − 4cos2x dx c) (4sinx + 2cosx)dx TSC-0-06-6992-2020-R00 MATHEMATICS LEVEL 4 2020-06-30 DPA/mlm Page 5

Recommend

Verifying Trigonometric Identities A trigonometric identity is simply an identity involving

Verifying Trigonometric Identities A trigonometric identity is simply an identity involving trigonometric functions. We learn to verify and spend time verifying trigonometric identities because the practice we get verifying trigonometric

661 views • 46 slides

Trigonometric Integrals Trigonometric Integrals There are four cases: Trigonometric Integrals

Trigonometric Integrals Trigonometric Integrals There are four cases: Trigonometric Integrals There are four cases: 1. Odd power of sin x or cos x : Trigonometric Integrals There are four cases: 1. Odd power of sin x or cos x : sin 3 xdx

831 views • 48 slides

Inverse Trigonometric Functions and Their Derivatives None of the trigonometric functions

Inverse Trigonometric Functions and Their Derivatives None of the trigonometric functions satisfies the horizontal line test, so none of them has an inverse. The inverse trigonometric functions are defined to be the inverses of particular parts

392 views • 22 slides

3. Trigonometry 3.1 Introduction to Trigonometry 3.2 Trigonometric Examples 3.3 Radians 3.4

3. Trigonometry 3.1 Introduction to Trigonometry 3.2 Trigonometric Examples 3.3 Radians 3.4 Periodicity and Plotting Trigonometric Functions 3.5 Major Trigonometric Identities 3.6 Inverse Trigonometric Functions 3.7 Domain and Range of

917 views • 80 slides

JUST THE MATHS SLIDES NUMBER 3.2 TRIGONOMETRY 2 (Graphs of trigonometric functions) by

JUST THE MATHS SLIDES NUMBER 3.2 TRIGONOMETRY 2 (Graphs of trigonometric functions) by A.J.Hobson 3.2.1 Graphs of elementary trigonometric functions 3.2.2 Graphs of more general trigonometric functions UNIT 3.2 - TRIGONOMETRY 2

100 views • 7 slides

JUST THE MATHS SLIDES NUMBER 3.1 TRIGONOMETRY 1 (Angles & trigonometric functions)

JUST THE MATHS SLIDES NUMBER 3.1 TRIGONOMETRY 1 (Angles & trigonometric functions) by A.J.Hobson 3.1.1 Introduction 3.1.2 Angular measure 3.1.3 Trigonometric functions UNIT 3.1 - TRIGONOMETRY 1 - ANGLES AND TRIGONOMETRIC

256 views • 9 slides

The Definite Integral The definite integral generalizes the concept of area. The Definite Integral

The Definite Integral The definite integral generalizes the concept of area. The Definite Integral The definite integral generalizes the concept of area. Lets begin with the physical intuition of this idea. The Definite Integral The definite

583 views • 40 slides

Math 104 Calculus 8.4 Trigonometric Subs=tu=ons Math 104

Math 104 Calculus 8.4 Trigonometric Subs=tu=ons Math 104 - Yu Trigonometric subs=tu=on Some=mes it is very helpful to use trigonometric

279 views • 13 slides

JUST THE MATHS SLIDES NUMBER 3.5 TRIGONOMETRY 5 (Trigonometric identities &

JUST THE MATHS SLIDES NUMBER 3.5 TRIGONOMETRY 5 (Trigonometric identities & wave-forms) by A.J.Hobson 3.5.1 Trigonometric identities 3.5.2 Amplitude, wave-length, frequency and phase-angle UNIT 3.5 - TRIGONOMETRY 5 TRIGONOMETRIC

425 views • 13 slides

d Derivative of Trigonometric Functions i E 2 Lectures a l l u d b Dr. Abdulla Eid A .

Section 3.5 d Derivative of Trigonometric Functions i E 2 Lectures a l l u d b Dr. Abdulla Eid A . College of Science r D MATHS 101: Calculus I Dr. Abdulla Eid (University of Bahrain) Trigonometric functions 1 / 23 d 1 Review

631 views • 23 slides

Right Triangle Trigonometry Special Right Triangles Trigonometric Functions Inverse

Chapter Three Right Triangle Trigonometry Special Right Triangles Trigonometric Functions Inverse Trigonometric Functions Special Right Triangles For all right triangles, a 2 + b 2 = c 2 , where a and b are the legs and c is the hypotenuse.

249 views • 4 slides

The Derivatives of the Trigonometric Functions Bernd Schr oder logo1 Bernd Schr oder

Two Limits Derivatives Examples The Derivatives of the Trigonometric Functions Bernd Schr oder logo1 Bernd Schr oder Louisiana Tech University, College of Engineering and Science The Derivatives of the Trigonometric Functions Two

1.11k views • 90 slides

Formal verification of floating point trigonometric functions John Harrison Intel Corporation

Formal verification of floating point trigonometric functions 1 Formal verification of floating point trigonometric functions John Harrison Intel Corporation Levels of verification HOL Light Theories of reals and floating point

268 views • 14 slides

Today we will be learning: -How to evaluate trigonometric functions of acute angles. -How to use

Today we will be learning: -How to evaluate trigonometric functions of acute angles. -How to use the fundamental trigonometric identities. Lesson 1.3 Rt. Trigonometry Sin = opp/hyp Opposite Cos = adj/hyp Side Tan = opp/adj

237 views • 9 slides

Derivatives of Trigonometric Functions Let f ( x ) = sin x . From the definition of a derivative, f

Derivatives of Trigonometric Functions Let f ( x ) = sin x . From the definition of a derivative, f ( x + h ) f ( x ) f ( x ) = lim h 0 = h sin( x + h ) sin x lim h 0 . h Conveniently, we have a trigonometric identity that

63 views • 3 slides

d Inverse Trigonometric Functions i E 1 Lecture a l l u d b Dr. Abdulla Eid A .

Section 3.9 d Inverse Trigonometric Functions i E 1 Lecture a l l u d b Dr. Abdulla Eid A . College of Science r D MATHS 101: Calculus I Dr. Abdulla Eid (University of Bahrain) Inverse Trig 1 / 20 Inverse Trigonometric

449 views • 20 slides

UDRC Summer School 2019 Day 2 - Sensing and Tracking David Cormack*, Mengwei Sun, James R.

UDRC Summer School 2019 Day 2 - Sensing and Tracking David Cormack*, Mengwei Sun, James R. Hopgood * drc9@hw.ac.uk University of Edinburgh 25 th June 2019 David Cormack, Mengwei Sun, James R. Hopgood Day 2 - Sensing and Tracking 1 / 96

2.17k views • 162 slides

2019 ANNUAL RESULTS FEBRUARY 2020 AGENDA Business overview Models Greenfields and

2019 ANNUAL RESULTS FEBRUARY 2020 AGENDA Business overview Models Greenfields and acquisitions History since 2011 Number of campuses Number of learners AGENDA Financial analysis Highlights December 2019

606 views • 34 slides

AAVAS FINANCIERS LIMITED Investor Presentation H1 FY19 October 2018 Safe Harbor This

AAVAS FINANCIERS LIMITED Investor Presentation H1 FY19 October 2018 Safe Harbor This presentation and the accompanying slides (the Presentation), which have been prepared by Aavas Financiers Ltd. (the Company), have been prepared

472 views • 43 slides

Discretionary Grants Overview of CATHSSETA Purpose Funding Framework

Discretionary Grants Overview of CATHSSETA Purpose Funding Framework Funding Criteria Pivotal Programmes 2017/18 Funding & Allocations 2018/19 Funding Framework Submission of application forms

441 views • 18 slides

No Excuse Vision Weekend October 27-28, 2018 Why Vision Weekend? Because vision is

No Excuse Vision Weekend October 27-28, 2018 Why Vision Weekend? Because vision is incredibly important and yet it chronically leaks (easy to get busy, distracted and forgetful vision needs to be continually re-infused in every

363 views • 14 slides

Thailand Biomass Pellets Update By Wattanapong Thongsoi info@bcex.org Topics Biomass (what,

Thailand Biomass Pellets Update By Wattanapong Thongsoi info@bcex.org Topics Biomass (what, why, type, form) Demand & Supply Standard and specification Cost Price Use locally & export Opportunity

590 views • 22 slides

Monitoring, Reporting and Verification for Emissions Trading: Challenges and Best Practices

www.ecologic.eu Monitoring, Reporting and Verification for Emissions Trading: Challenges and Best Practices Challenges and Best Practices Benjamin Grlach Ecologic Institute EU-China Exchange on Challenges and Best Practices in ETS MRV

527 views • 26 slides

AGRUCULTURBUSINES MANAGEMENT ( INTEGATED COURSE) B Sc/ DIPLOMA NAUTICAL SCIENCE FIRE SAFETY

MARITIME EDUCATION : B.TECH. MARINE .ENGINEERING : B.TECH.MECHANICAL .ENGINEERING : B.TECH.HARBOUR &OCEAN ENGINEERING : B.TECH.NA V AL ARCHITECTURE &OFFSHORE ENG : BSC .SHIP BUILDING &REP AIR : B.B.A . SHIPPING &

385 views • 15 slides