Inverse Trigonometric Functions

Jul 27, 2014

190 likes | 476 Vues

Inverse Trigonometric Functions. Properties of Inverse Trigonometric Functions. Principal value branches of inverse trigonometric functions. Properties of Inverse Trigonometric Functions. Properties of Inverse Trigonometric Functions. Properties of Inverse Trigonometric Functions.

Share Presentation

Embed Code

Link

hanh

Télécharger la présentation

Inverse Trigonometric Functions

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

Inverse Trigonometric Functions Properties of Inverse Trigonometric Functions
Principal value branches of inverse trigonometric functions

Properties of Inverse Trigonometric Functions
Properties of Inverse Trigonometric Functions
Properties of Inverse Trigonometric Functions
Properties of Inverse Trigonometric Functions
Properties of Inverse Trigonometric Functions
Properties of Inverse Trigonometric Functions

Inverse Trigonometric Functions

Inverse Trigonometric Functions. 4.7. Definition of Inverse Sine Function. The inverse sine function is defined by y = arcsin x if and only if sin y = x where -1 ≤ x ≤ 1 and – π /2 ≤ y ≤ π /2. The domain of y = arcsin x is [-1, 1] and the range is [ - π /2 , π /2]. . What does this mean?.

545 views • 11 slides

4.8 Inverse Trigonometric Functions

The inverse trig functions. Inverse trig functions are not ?true" inverses? Instead, each inverse trig function has a domain that is restricted to intervals where the function is one-to-one and where they have the same range as the ordinary trig functions.Remember from Section 2.5, functions that

1.05k views • 35 slides

The inverse trigonometric functions

The inverse trigonometric functions. The inverse trigonometric functions The reciprocal trigonometric functions Trigonometric identities Examination-style question. Contents. 1 of 35. © Boardworks Ltd 2006. The inverse of the sine function.

1.18k views • 11 slides

Inverse Trigonometric Functions

Inverse Trigonometric Functions. Section 4.7. Objectives. Evaluate inverse trigonometric functions at given values. State the domain and range of each of the inverse trigonometric functions.

1.38k views • 39 slides

3.5 Inverse Trigonometric Functions

3.5 Inverse Trigonometric Functions. Inverse sine (or arcsine) function. f(x)=sin x is not one-to-one

596 views • 6 slides

Inverse Trigonometric Functions: Integration

Inverse Trigonometric Functions: Integration. Lesson 5.8. Review. Recall derivatives of inverse trig functions. Integrals Using Same Relationships. When given integral problems, look for these patterns. Identifying Patterns.

1.16k views • 31 slides

Inverse Trigonometric Functions

Inverse Trigonometric Functions. Properties and Formulae. ANIL SHARMA K.V. HIRA NAGAR. we have studied that the inverse of a function f, denoted by f –1, exists if f is one-one and onto. There are many functions which are not one-one, onto or both and

1.07k views • 19 slides

13.4 Inverse Trigonometric Functions

13.4 Inverse Trigonometric Functions. Algebra 2. Inverse Trigonometric Functions. If -1≤a≤1, then the inverse sine of a is sin -1 a= θ where sin θ =a and -90˚≤ θ≤ 90 ˚ . If -1 ≤ a, then the inverse cosine of a is cos -1 a= θ and -0 ˚≤θ≤ 180 ˚ .

316 views • 16 slides

Inverse Trigonometric Functions 4.7

Inverse Trigonometric Functions 4.7. How do you determine if a function has an inverse?. It must be one to one … pass the horizontal line test Will a sine, cosine, or tangent function have an inverse? Their inverses are defined over the following intervals: Sine: [ - π /2, π /2 ]

390 views • 15 slides

8.2 Inverse Trigonometric Functions

Why are we learning this? We can solve trigonometric equations using inverse trigonometric functions How did we solve before?. 8.2 Inverse Trigonometric Functions. Function test for y=x, y=x 2 , y= sinx. Let us restrict the domain!. Learning Targets: Review Inverse functions

433 views • 8 slides

Inverse Trigonometric Functions

Inverse Trigonometric Functions. M 140 Precalculus V. J. Motto. Let us remember our discussion on inverse functions:. We found inverses for functions by Reversing ordered pairs: (x, y)  (y, x) Reflection the function f across the line y = x Showing that (fog)(x) = x. Then g = f -1.

1.67k views • 31 slides

Inverse Trigonometric Functions

Inverse Trigonometric Functions. Recall some facts about inverse functions: For a function to have an inverse it must be a one-to-one function. The domain of f -1 is the range of f . The range of f -1 is the domain of f .

1.96k views • 13 slides

Inverse Trigonometric Functions

Inverse Trigonometric Functions. Trigonometry MATH 103 S. Rook. Overview. Section 4.7 in the textbook: Review of inverse functions Inverse sine function Inverse cosine function Inverse tangent function Inverse trigonometric functions and right triangles. Review of Inverse Functions.

894 views • 27 slides

4.7 Inverse Trigonometric Functions

4.7 Inverse Trigonometric Functions. Definition of the Inverse Trig. Functions. 1. arcsin x quadrants I and IV. 2. arccos x quadrants I and II. 3. arctan x quadrants I and IV. Find the values of :. -1. I or IV. 2. 2. I or IV. 1. I or II. 1. 1. 1. 0. -1.

759 views • 8 slides

4.7 Inverse Trigonometric functions

4.7 Inverse Trigonometric functions. Arcsine Arccosine. Lets review inverse functions. Find the inverse of f(x) = 3x + 6 y = 3x + 6 Inverse functions switch domain and range. So, x = 3y + 6 ( solve for y) x – 6 = 3y ⅓ x – 2 = y f -1 (x) = ⅓ x - 2.

425 views • 22 slides

Inverse Trigonometric Functions

Inverse Trigonometric Functions. For Arccos x , Arcsec x , and Arccot x. For Arcsin x , Arccsc x , and Arctan x. +I. -I.

500 views • 10 slides

4.7 Inverse Trigonometric Functions

4.7 Inverse Trigonometric Functions. Inverse functions. g(x) is the inverse function of f(x) IF g(f(x)) = x and f(g(x)) = x We notate an inverse function as f -1 (x) Example f(x) = 4x f -1 (x)=. Remember your favorite inverse functions?.

472 views • 19 slides

4.7 Inverse Trigonometric Functions

4.7 Inverse Trigonometric Functions. *Intro to Inverse Functions *One-to-one *Inverse of Sine. Inverse Functions. f -1 (x) is the inverse of f(x) If and only if the domain of f(x) is equal to the range of f -1 (x) AND the range of f(x) is equal to the domain of f -1 (x)

250 views • 12 slides

3.9 – Inverse Trigonometric Functions

3.9 – Inverse Trigonometric Functions. 3.9 – Inverse Trigonometric Functions. 3.9 – Inverse Trigonometric Functions. 3.9 – Inverse Trigonometric Functions. 3.11 – Linearization and Differentials. 3.11 – Linearization and Differentials. 3.11 – Linearization and Differentials.

467 views • 17 slides

Inverse Trigonometric Functions

Inverse Trigonometric Functions. We will now formalize what we have been doing informally throughout this chapter. Review of Inverse Functions. They “undo” one another. Can you name some? What is the inverse of y = 2x + 3? x and y are interchanged They are symmetrical around the line y = x.

343 views • 12 slides

Inverse Trigonometric Functions 4.7

Inverse Trigonometric Functions 4.7. y. y = sin x -  / 2 < x <  / 2. 1. -  / 2. x.  / 2. -1. Domain : [ -  / 2 ,  / 2 ] Range : [ -1, 1 ]. The Inverse Sine Function.

283 views • 20 slides

INVERSE TRIGONOMETRIC FUNCTIONS

INVERSE TRIGONOMETRIC FUNCTIONS. What is the first pair of inverse functions that pop into YOUR mind?. This is a famous pair. But something is not quite right with this pair. Do you know what is wrong?.

438 views • 27 slides

More Related