Presentation is loading. Please wait.

Presentation is loading. Please wait.

TRIGONOMETRIC SUBSTITUTION. NOTE: We convert the radical into a cos function.

Published byNeil Simmons Modified over 9 years ago

Similar presentations

Presentation on theme: "TRIGONOMETRIC SUBSTITUTION. NOTE: We convert the radical into a cos function."— Presentation transcript:

1 TRIGONOMETRIC SUBSTITUTION

2 NOTE: We convert the radical into a cos function

3 TRIGONOMETRIC SUBSTITUTION

4 Example Find Example Find Example Find The main idea is how to get rid of the radicals. ( use trig. Substitution)

5 TRIGONOMETRIC SUBSTITUTION Expression

6 TRIGONOMETRIC SUBSTITUTION Example Find In the following table we list trigonometric substitutions that are effective for the given radical expressions because of the specified trigonometric identities.

7 TRIGONOMETRIC SUBSTITUTION Example Find In the following table we list trigonometric substitutions that are effective for the given radical expressions because of the specified trigonometric identities.

8 TRIGONOMETRIC SUBSTITUTION Example Find

9 TRIGONOMETRIC SUBSTITUTION Example Find

10 TRIGONOMETRIC SUBSTITUTION EXAM-2 Term-092

11 TRIGONOMETRIC SUBSTITUTION Example Find

12 TRIGONOMETRIC SUBSTITUTION EXAM-2 Term-102

13 TRIGONOMETRIC SUBSTITUTION Example Find hyperbolic substitutions can be used in place of trigonometric substitutions and sometimes they lead to simpler answers. But we usually use trigonometric substitutions because trigonometric identities are more familiar than hyperbolic identities.

14 TRIGONOMETRIC SUBSTITUTION Example Find

15

16

17

18

19

20

21

Download ppt "TRIGONOMETRIC SUBSTITUTION. NOTE: We convert the radical into a cos function."

Similar presentations

Using Fundamental Identities

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

Integration Using Trigonometric Substitution Brought to you by Tutorial Services – The Math Center.
Trig Graphs. y = sin x y = cos x y = tan x y = sin x + 2.

Trig Graphs. y = sin x y = cos x y = tan x y = sin x + 2.
Write the following trigonometric expression in terms of sine and cosine, and then simplify: sin x cot x Select the correct answer: 1234567891011121314151617181920.

Write the following trigonometric expression in terms of sine and cosine, and then simplify: sin x cot x Select the correct answer:
6.2 Trigonometric Integrals. How to integrate powers of sinx and cosx (i) If the power of cos x is odd, save one cosine factor and use cos 2 x = 1 - sin.

6.2 Trigonometric Integrals. How to integrate powers of sinx and cosx (i) If the power of cos x is odd, save one cosine factor and use cos 2 x = 1 - sin.
TECHNIQUES OF INTEGRATION

TECHNIQUES OF INTEGRATION
The Method of Trigonometric Substitution. Main Idea The method helps dealing with integrals, where the integrand contains one of the following expressions:

The Method of Trigonometric Substitution. Main Idea The method helps dealing with integrals, where the integrand contains one of the following expressions:
Warm up  If, find.  Express cos 490o as a trig function of an angle in Quadrant 1.  Simplify.

Warm up  If, find.  Express cos 490o as a trig function of an angle in Quadrant 1.  Simplify.
Essential Question: How do we find the non-calculator solution to inverse sin and cosine functions?

Essential Question: How do we find the non-calculator solution to inverse sin and cosine functions?
5.3 Solving Trigonometric Equations. What are two values of x between 0 and When Cos x = ½ x = arccos ½.

5.3 Solving Trigonometric Equations. What are two values of x between 0 and When Cos x = ½ x = arccos ½.
Trig Identities.

Trig Identities.
Objective: Develop basic trigonometric identities.

Objective: Develop basic trigonometric identities.
Verifying Trigonometric Identities T,3.2: Students prove other trigonometric identities and simplify others by using the identity cos 2 (x) + sin 2 (x)

Verifying Trigonometric Identities T,3.2: Students prove other trigonometric identities and simplify others by using the identity cos 2 (x) + sin 2 (x)
EXAMPLE 1 Find trigonometric values Given that sin  = and <  < π, find the values of the other five trigonometric functions of . 4 5 π 2.

EXAMPLE 1 Find trigonometric values Given that sin  = and <  < π, find the values of the other five trigonometric functions of . 4 5 π 2.
What you will learn How to use the basic trigonometric identities to verify other (more complex) identities How to find numerical values of trigonometric.

What you will learn How to use the basic trigonometric identities to verify other (more complex) identities How to find numerical values of trigonometric.
Lesson 7-2 Hard Trig Integrals. Strategies for Hard Trig Integrals ExpressionSubstitutionTrig Identity sin n x or cos n x, n is odd Keep one sin x or.

Lesson 7-2 Hard Trig Integrals. Strategies for Hard Trig Integrals ExpressionSubstitutionTrig Identity sin n x or cos n x, n is odd Keep one sin x or.
5.1 Using Fundamental Identities. Fundamental Trigonometric Identities.

5.1 Using Fundamental Identities. Fundamental Trigonometric Identities.
5.1 Using Fundamental Identities

5.1 Using Fundamental Identities
Sum and Difference Formulas New Identities. Cosine Formulas.

Sum and Difference Formulas New Identities. Cosine Formulas.
Section 5.1 Verifying Trigonometric Identities.

Section 5.1 Verifying Trigonometric Identities.

Similar presentations

Ads by Google