AP Calculus BC Wednesday, 09 March 2016 OBJECTIVE TSW (1) solve integrals using trig substitution, and (2) quiz over basic integration rules and integration.

Slides:

Advertisements

Similar presentations

Integration Using Trigonometric Substitution Brought to you by Tutorial Services – The Math Center.

Advertisements

Right Triangle Trigonometry

AP Calculus BC Monday, 18 November 2013 OBJECTIVE TSW use integration by subsitution. ASSIGNMENT DUE –Sec. 4.1  wire basket Tests are graded. Look on.

Today – Monday, March 4, 2013  Warm Up: Which method to use to solve missing angles or sides of a right triangle  Review: Using inverse trig to find.

Section 4 Inverses of the Trigonometric Functions

TECHNIQUES OF INTEGRATION

The Pythagorean Theorem From The Simpson’s Homer copies the Scarecrow on The Wizard of Oz.

TODAY IN GEOMETRY…  Review: Methods solving for missing sides of a right triangle  Learning Target: 7.6 Finding an angle using inverse Trigonometry 

9.6 Solving Right Triangles Geometry Mrs. Spitz Spring 2005.

Trigonometry Chapters Theorem.

TODAY IN ALGEBRA 2.0…  Review: Pythagorean Theorem  Learning Target: Find all six trigonometric functions.  Independent Practice.

Chapter 3 Trigonometric Functions of Angles Section 3.2 Trigonometry of Right Triangles.

Warm - Up Find the measure(s) of

Right Triangle Trigonometry

Geometry One is always a long way from solving a problem until one actually has the answer. Stephen Hawking Today: ACT VOCAB CHECK 8.4 Cont. Practice.

Right Triangle Trigonometry

Warm-Up 3/24-25 What are three basic trigonometric functions and the their ratios? Sine: sin  Cosine: cos  Tangent: tan 

AP Calculus BC Wednesday, 09 September 2015 OBJECTIVE TSW review for Friday’s test covering chapter 2. TO RECEIVE A DROP DAILY GRADE ON FRIDAY –Wear a.

The midpoint of is M(-4,6). If point R is (6, -9), find point J.

AP Calculus BC Monday, 14 September 2015 OBJECTIVE TSW (1) define the slope of a curve at a point, and (2) define the derivative. Tests are graded. TODAY’S.

AP Calculus BC Monday, 21 September 2015 OBJECTIVES TSW find (1) derivatives using the product and quotient rules, and (2) higher-order derivatives. ASSIGNMENT.

Aim: Differentiate Inverse Trig Functions Course: Calculus Do Now: Aim: How do we differentiate Inverse Trig functions? Does y = sin x have an inverse?

Geometry One is always a long way from solving a problem until one actually has the answer. Stephen Hawking Today: ACT VOCAB CHECK 9.6 Instruction Practice.

13.1 Trigonometric Identities

4.7 Inverse Trig Functions. By the end of today, we will learn about….. Inverse Sine Function Inverse Cosine and Tangent Functions Composing Trigonometric.

5.2 Trigonometric Ratios in Right Triangles

The Right Triangle Right Triangle Pythagorean Theorem

1 7.2 Right Triangle Trigonometry In this section, we will study the following topics: Evaluating trig functions of acute angles using right triangles.

Integrals of the Form: Chapter 7.3 March 27, 2007.

AP Calculus BC Monday, 31 August 2015 OBJECTIVE TSW find infinite limits FORM DUE (only if it is signed) –Information Sheet (wire basket) If you have t-shirt.

Exponential Functions – Differentiation and Integration.

Chapter 7 – Techniques of Integration 7.3 Trigonometric Substitution 1Erickson.

AP Calculus BC Friday, 05 February 2016 OBJECTIVE TSW (1) explore properties of inverse trigonometric functions, (2) differentiate inverse trig functions,

Chapter 4 Section 3 Right triangle trigonometry. Objectives Evaluate trigonometric functions of acute angles Use fundamental trigonometric identities.

Trigonometry 2 Finding the angle when the sides are given.

Splash Screen. Then/Now You used the Pythagorean Theorem. Find trigonometric ratios of angles. Use trigonometry to solve triangles.

Trigonometric Ratios Section 8.1. Warm Up State the following: 1.Angle opposite AB 2.Side opposite angle A 3.Side opposite angle B 4.Angle opposite AC.

Material Taken From: Mathematics for the international student Mathematical Studies SL Mal Coad, Glen Whiffen, John Owen, Robert Haese, Sandra Haese and.

Trig Functions – Part Pythagorean Theorem & Basic Trig Functions Reciprocal Identities & Special Values Practice Problems.

AP Calculus BC Tuesday, 09 February 2016 OBJECTIVE TSW review for tomorrow's test differentiation and integration of transcendental functions and their.

OBJECTIVE TSW (1) list the terms of a sequence; (2) determine whether a sequence converges or diverges; (3) write a formula for the nth term of a sequence;

13.1 Right Triangle Trigonometry ©2002 by R. Villar All Rights Reserved.

OBJECTIVE TSW (1) evaluate improper integrals, and (2) review for the test covering integration techniques. ASSIGNMENT DUE TOMORROW, FRIDAY, 04/01/16 –Improper.

1 College Algebra K/DC Friday, 09 October 2015 OBJECTIVE TSW reduce and simplify expressions with rational exponents. (Students will receive their own.

5.2 Trigonometric Ratios in Right Triangles. A triangle in which one angle is a right angle is called a right triangle. The side opposite the right angle.

Derivatives of Inverse Trigonometric Functions. Integrals.

Right Triangle Trigonometry

A triangle in which one angle is a right angle is called a right triangle. The side opposite the right angle is called the hypotenuse, and the remaining.

Integration Using Trigonometric Substitution

Section 4.7 Inverse Trigonometric Functions

Integration by Substitution

…there are three trig ratios

…there are three trig ratios

Bell work: Find the missing side for the triangles below

Warm – Up: 2/4 Convert from radians to degrees.

Trigonometric Functions

Unit 3: Right Triangle Trigonometry

Lesson 7-3 Trig Substitution.

Right Triangle Ratios Chapter 6.

Review these 1.) cos-1 √3/ ) sin-1-√2/2 3.) tan -1 -√ ) cos-1 -1/2

Right Triangle Trigonometry

Trig. Ratios in a Coordinate System

Group Thinking – CIC Problem

Right Triangle Trigonometry

Introduction to Trigonometric Functions

…there are three trig ratios

Right Triangle Trigonometry

Presentation transcript:

AP Calculus BC Wednesday, 09 March 2016 OBJECTIVE TSW (1) solve integrals using trig substitution, and (2) quiz over basic integration rules and integration by parts. ASSIGNMENT DUE –Integration by Parts  wire basket ASSIGNMENTS DUE FRIDAY, 03/11/16 –Trigonometric Integrals –WS Integrals of Sine-Cosine Products TODAY’S ASSIGNMENT (due Monday, 03/22/16, but turn in on Friday, 03/11/16) –Trigonometric Substitution REMINDERS Friday, 11 March 2016 –PI Day Celebration: Friday, 11 March 2016

AP Calculus BC Thursday, 10 March 2016 OBJECTIVE TSW (1) solve integrals using trig substitution, and (2) quiz over basic integration rules and integration by parts. ASSIGNMENT DUE –Integration by Parts  wire basket ASSIGNMENTS DUE TOMORROW, 03/11/16 –Trigonometric Integrals –WS Integrals of Sine-Cosine Products TODAY’S ASSIGNMENT (due Monday, 03/22/16, but turn in tomorrow, 03/11/16) –Trigonometric Substitution REMINDERS Friday, 11 March 2016 –PI Day Celebration: Friday, 11 March 2016

Trigonometric Substitution (due Monday, 03/22/16)* Evaluate the following integrals. Evaluate the following definite integrals. *I would suggest turning this in on Friday!!!

Trigonometric Substitution

The idea of this section is to evaluate integrals with radicals of the form This will be done using the three Pythagorean identities:

1)For integrals involving Trigonometric Substitution (a > 0) Trigonometric Substitution a u  This looks like arcsin. The sin ratio is opposite / hypotenuse. "a" should go on the hypotenuse; "u" should go on the opposite side; the square root goes on the remaining side.

Trigonometric Substitution Ex:Evaluate: 3 x θ

2)For integrals involving Trigonometric Substitution (a > 0) Trigonometric Substitution a u  This looks like arctan. The tan ratio is opposite / adjacent. "a" should go on the adjacent side; "u" should go on the opposite side; the square root goes on the remaining side.

Trigonometric Substitution Ex:Evaluate: θ 1 2x2x

3)For integrals involving Trigonometric Substitution (a > 0) Trigonometric Substitution a u  This looks like arcsec. The sec ratio is hypotenuse / adjacent. "a" should go on the adjacent side; "u" should go on the hypotenuse; the square root goes on the remaining side.

Trigonometric Substitution Ex:Evaluate: θ x

Trigonometric Substitution Ex:Evaluate: θ x

Trigonometric Substitution Ex:Evaluate: θ x 2

Trigonometric Substitution Ex:Evaluate: θ x

Trigonometric Substitution Ex:Evaluate: θ x – 2 Completing the Square 2

QUIZ: Basic Integration Rules, Integration by Parts You may use a calculator. You have the remainder of the period to take the quiz. ASSIGNMENTS DUE FRIDAY, 03/11/16  Trigonometric Integrals  WS Integrals of Sine-Cosine Products (due Monday, 03/21/16, but suggested to turn in on Friday, 03/11/16)  Trigonometric Substitution (due Monday, 03/21/16, but suggested to turn in on Friday, 03/11/16) Sallie says, “Take my quiz!!”

QUIZ: Basic Integration Rules, Integration by Parts You may use a calculator. You have the remainder of the period to take the quiz. ASSIGNMENTS DUE TOMORROW, 03/11/16  Trigonometric Integrals  WS Integrals of Sine-Cosine Products (due Monday, 03/21/16, but suggested to turn in tomorrow, 03/11/16)  Trigonometric Substitution (due Monday, 03/21/16, but suggested to turn in tomorrow, 03/11/16) Sallie says, “Take my quiz!!”