4.7 Inverse Trigonometric Functions

Slides:

Advertisements

Similar presentations

4.7 Inverse Trig Functions. Does the Sine function have an inverse? 1.

Advertisements

Sullivan Precalculus: Section 5.2 Trig Functions: Unit Circle

Section 4.7 Inverse Trigonometric Functions. A brief review….. 1.If a function is one-to-one, the function has an inverse that is a function. 2.If the.

Chapter 5: Trigonometric Functions Lessons 3, 5, 6: Inverse Cosine, Inverse Sine, and Inverse Tangent functions Mrs. Parziale.

Starter a 6 c A 53° 84° 1.Use Law of Sines to calculate side c of the triangle. 2.Use the Law of Cosines to calculate side a of the triangle. 3.Now find.

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

Find the exact values:. Inverse Trig Functions Inverse: “the angle whose (trig function) is x” Arcsin x or [-90° to 90°] Arccos x or [0° to 180°] Arctan.

Inverse Trig Functions Learning Goals: 1.Understand Domain/Range requirements for inverse trig functions 2.Be able to calculate exact values for inverse.

4.7 Inverse Trig Functions

TODAY IN ALGEBRA 2.0…  Review: Pythagorean Theorem and the six trigonometric functions  Learning Target: 13.1 You will find missing sides of a triangle.

TODAY IN ALGEBRA 2.0…  Review: Solving for a given side  Learning Target: 13.1 Finding an angle using inverse Trigonometry  Independent Practice.

 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 Inverse Cosine Function Lesson 5.3. Reminder… y = cos x.

Section 5.5 Inverse Trigonometric Functions & Their Graphs

Derivatives of Inverse Trigonometric Functions

Section 6.4 Inverse Trigonometric Functions & Right Triangles

Precalculus 4.7 Inverse Trigonometric Functions 1 Inverse functions ·Do all functions have an inverse? ·Only functions that are monotonic (always increasing.

20 Days. Three days  Graphing Sine and Cosine WS.

Copyright © 2011 Pearson, Inc. 4.7 Inverse Trigonometric Functions.

Chapter 4 Trigonometric Functions Inverse Trigonometric Functions Objectives:  Evaluate inverse sine functions.  Evaluate other inverse trigonometric.

4.7 INVERSE TRIGONOMETRIC FUNCTIONS. For an inverse to exist the function MUST be one- to - one A function is one-to- one if for every x there is exactly.

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

TODAY IN GEOMETRY…  Review: SOH CAH TOA  Learning Target 1: 7.4 You will find missing sides of a triangle using TRIG  Independent Practice  Learning.

1 8.1 Inverse Trigonometric Functions In this section, we will study the following topics: Definitions of the inverse trig functions Evaluating inverse.

Values of the Trig Functions Reference angles and inverse functions (5.4)

Inverse Trig Functions Objective: Evaluate the Inverse Trig Functions.

Inverse Trigonometric

Section 4.7 Inverse Trigonometric Functions Pg

4.7 Inverse Trigonometric functions

Inverse Trigonometric Functions. Copyright © by Houghton Mifflin Company, Inc. All rights reserved. 2 HWQ Write a sine equation that has an amplitude.

Pg. 385 Homework Pg. 395#13 – 41 odd, Graph the three inverse trig functions and label the domain and range of each. Memorization quiz through inverse.

OBJECTIVES: Evaluate the inverse trigonometric functions Evaluate the compositions of trigonometric functions.

Solving for (3 Ways). Examples Without using a calculator, what angle(s) would satisfy the equation ?

February 6, 2012 At the end of today, you will be able to understand inverse trig functions. Warm-up: Trig Review without a calculator

Warm-up – 9/18/2015 Do your warm-up in your notes 1) 2) 3)

Chapter 4 Trigonometric Functions The Unit Circle Objectives:  Evaluate trigonometric functions using the unit circle.  Use domain and period.

Pg. 395 Homework Pg. 395#1 – 10 all Pg. 401#19 – 23 odd Pg. 407#9 Memorization quiz Thursday!! # °#157.13°# #191.17#21π/2#23π/4 #25-π/3#270.36#

2.5 Cont. Warm-up (IN) Learning Objective: To know the domain and range of the trig functions, and to use the Even-Odd Properties to find the Exact values.

Precalculus Chapter 5.1 Using Fundamental Identities Objectives: Recognize and write trig identities Use trig identities to evaluate, simplify, and rewrite.

Sullivan Precalculus: Section 5.3 Properties of the Trig Functions Objectives of this Section Determine the Domain and Range of the Trigonometric Functions.

Section Inverse Sine and Cosine. Lesson Objective: Students will: Graph the relations for inverse sine and cosine. Restrict the range for to make.

Section 4.7 Inverse Trigonometric Functions. Helpful things to remember. If no horizontal line intersects the graph of a function more than once, the.

ANSWERS. Using Trig in every day life. Check Homework.

7.4 Inverse Trig Functions. For a function to have an inverse it must be one-to- one. One-to-one functions have to pass the horizontal line test. Each.

Try this Locate the vertical asymptotes and sketch the graph of y = 2 sec x. 2. Locate the vertical asymptotes and sketch the graph of y = 3 tan.

5.7 Inverse Trig Functions. Does the sine function have an inverse?

Precalculus 4.3 Right Triangle Trigonometry 1 Bellwork Rationalize the denominators ·

4.4 Trig Functions of Any Angle Objectives: Evaluate trigonometric functions of any angle Use reference angles to evaluate trig functions.

4.7(b) Notes: The Other Inverse Trig. Functions

Inverse Trigonometric Functions

Find the exact values:.

Section 4.7 Inverse Trigonometric Functions

What are the amplitude, period, and translations of: y=2sin(2x-π)-3

Trig/Precalc Chapter 5.7 Inverse trig functions

Inverse Trigonometric: Integration

Warm Up Let g(x) = {(1, 3), (2, 5), (4, 10), (-3, 7)}. What is g -1(x)? Write the inverse of the function: f(x) = 2x – 3 Determine whether the function.

Find the exact values:.

Homework Log Fri 5/6 Lesson 8 – 7 Learning Objective:

Section 1.7 Inverse Trigonometric Functions

Inverse Trigonometric Functions

Inverse Trigonometric Functions

Trigonometric Functions: The Unit Circle (Section 4-2)

Warm-up: Find the exact values of the other 5 trigonometric functions given sin= 3 2 with 0 <  < 90 CW: Right Triangle Trig.

Trigonometric Functions: The Unit Circle

Inverse Trigonometric Functions

Warm-up Put the problems from the homework up on the board that you wish to review Textbook pages #5-23 ODD, 59 and 61.

Let’s think about the function f() = sin 

Sum and Difference Formulas (Section 5-4)

Presentation transcript:

4.7 Inverse Trigonometric Functions Bellwork Use your unit circle to find the possible values of  Keep the unit circle handy for reference during today’s notes Talk about there being more than one answer for each Precalculus 4.7 Inverse Trigonometric Functions

4.7 Inverse Trig Functions Objectives: Identify the domain and range of the inverse trigonometric functions Use inverse trig functions to find angles Evaluate combinations of trig functions

4.7 Inverse Trigonometric Functions Calculator Practice Use your calculator to evaluate the three problems from bellwork Do the calculator answers match your answers from the unit circle? Talk about radian mode vs degree mode Talk about finding more than one answer on the unit circle Precalculus 4.7 Inverse Trigonometric Functions

Inverse Sine Function: Arcsin The calculator can’t display two values In order to be a function, each input can only have one output Look at unit circle together Precalculus 4.7 Inverse Trigonometric Functions

4.7 Inverse Trigonometric Functions The inverse sine graph Precalculus 4.7 Inverse Trigonometric Functions

Inverse Cosine Function: Arccos Look at unit circle Precalculus 4.7 Inverse Trigonometric Functions

4.7 Inverse Trigonometric Functions Example Precalculus 4.7 Inverse Trigonometric Functions

4.7 Inverse Trigonometric Functions Example Find the exact value. Precalculus 4.7 Inverse Trigonometric Functions

4.7 Inverse Trigonometric Functions Example Find the exact value (when possible) Arctan (-5) is ok 5pi/3 is not doable, but it is coterminal with -pi/3 which is Pi is not in the domain of the inverse cosine Precalculus 4.7 Inverse Trigonometric Functions

4.7 Inverse Trigonometric Functions Example Find the exact value of  x y Place triangle based on properties of inverse function Precalculus 4.7 Inverse Trigonometric Functions

4.7 Inverse Trigonometric Functions Example Find the exact value of  x y Place triangle based on properties of inverse function Precalculus 4.7 Inverse Trigonometric Functions

4.7 Inverse Trigonometric Functions Assignments Classwork (You Try) Label assignment CW 4.7 Pg. 351: #5-15 odd, 19-23 odd, 27-53 odd, 71 Homework Label assignment HW 4.7 Pg. 351: #24, 26,32, 48, 56 (full write-up), 72, 80-83 all Precalculus 4.7 Inverse Trigonometric Functions