© Annie Patton Differentiation of Inverse Trigonometric Function Next Slide.

Slides:



Advertisements
Similar presentations
© Annie Patton Differentiation by First Principles Next Slide.
Advertisements

© Annie Patton 2007 Paper 1 No 7 Next Slide. © Annie Patton Leaving Certificate 2007 Higher Level Paper 1 no 7(a) Start clicking when you want to see.
Trigonometric Identities
Inverse Trigonometric Functions Recall some facts about inverse functions: 1.For a function to have an inverse it must be a one-to-one function. 2.The.
Trig Graphs. y = sin x y = cos x y = tan x y = sin x + 2.
1 Special Angle Values. 2 Directions A slide will appear showing a trig function with a special angle. Work out the answer Hit the down arrow to check.
Special Triangles: 45 o -45 o -90 o ° x x Example: 45° 7 7 x x.
1 Special Angle Values. 2 Directions A slide will appear showing a trig function with a special angle. Work out the answer Hit the down arrow to check.
1 Special Angle Values DEGREES. 2 Directions A slide will appear showing a trig function with a special angle. Say the value aloud before the computer.
3.5 Inverse Trigonometric Functions
Write the following trigonometric expression in terms of sine and cosine, and then simplify: sin x cot x Select the correct answer:
Brief insight.  3.1 Understand mathematical equations appropriate to the solving of general engineering problems  3.2 Understand trigonometric functions.
QUADRANT I THE UNIT CIRCLE. REMEMBER Find the length of the missing side: x y x y x y Aim: Use the unit circle in order to find the exact value.
Find the period of the function y = 4 sin x
Trigonometric equations
5.3 Solving Trigonometric Equations. What are two values of x between 0 and When Cos x = ½ x = arccos ½.
5-5 Solving Right Triangles. Find Sin Ѳ = 0 Find Cos Ѳ =.7.
3.8 Derivatives of Inverse Trigonometric Functions.
EXAMPLE 1 Use an inverse tangent to find an angle measure
5.5 Multiple-Angle and Product-Sum Formulas. Find all solutions in.
Trigonometric Equations Edited by Mr. Francis Hung Last Updated: 2013–03–12 1http:///
CHAPTER Continuity Integration by Parts The formula for integration by parts  f (x) g’(x) dx = f (x) g(x) -  g(x) f’(x) dx. Substitution Rule that.
© Annie Patton Parametric Functions Next Slide. © Annie Patton Aim of Lesson To establish what is a set of Parametric Functions and how to differentiate.
 3.8 Derivatives of Inverse Trigonometric Functions.
Sum and Difference Formulas New Identities. Cosine Formulas.
Trigonometric Equations Edited by Mr. Francis Hung Last Updated:
© Annie Patton Implicit Functions Next Slide. © Annie Patton Aim of Lesson Next Slide To establish, what is an Implicit Function and how to differentiate.
Inverse Trigonometric Functions 4.7
Chapter 4 Trigonometric Functions Inverse Trigonometric Functions Objectives:  Evaluate inverse sine functions.  Evaluate other inverse trigonometric.
Asymptotes Next slide © Annie Patton.
2.4 The Chain Rule Remember the composition of two functions? The chain rule is used when you have the composition of two functions.
CHAPTER Continuity Implicit Differentiation.
4.7 Inverse Trig Functions. By the end of today, we will learn about….. Inverse Sine Function Inverse Cosine and Tangent Functions Composing Trigonometric.
4.4 Trigonometric Functions of Any Angle
Evaluating Inverse Trigonometric Functions
© Annie Patton Newton-Raphson Method Next Slide. © Annie Patton Aim of lesson To learn how the Newton- Raphson method can be used for finding non integer.
Solving Trigonometric Equations T, 11.0: Students demonstrate an understanding of half-angle and double- angle formulas for sines and cosines and can use.
Notes Over 6.3 Evaluating Trigonometric Functions Given a Point Use the given point on the terminal side of an angle θ in standard position. Then evaluate.
© Annie Patton Differentiation of Products Next Slide.
Sum and Difference Formulas...using the sum and difference formula to solve trigonometric equation.
Unit 4: Trigonometry Minds On. Unit 4: Trigonometry Minds On.
Solving Right Triangles Use trigonometric ratios to find angle measures in right triangles and to solve real-world problems.
Warm-Up Write the sin, cos, and tan of angle A. A BC
On the screens click on the number you think is the right answer. Three times tables Good luck!
Aim #7.1: What is the difference between direct and inverse variation? The equation y =ax represents direct variation between x and y. Y is said to vary.
(1) Sin, Cos or Tan? x 7 35 o S H O C H A T A O Answer: Tan You know the adjacent and want the opposite.
Simplify the following trigonometric expression as much as possible: cos B + sin B tan B Select the correct answer:
EXAMPLE 1 Evaluate trigonometric expressions Find the exact value of (a) cos 165° and (b) tan. π 12 a. cos 165° 1 2 = cos (330°) = – 1 + cos 330° 2 = –
Sin x = Solve for 0° ≤ x ≤ 720°
Pg. 384/408 Homework See later slide. #2V stretch 3, H stretch 2, V shift up 2, H shift left π #4V Stretch 2, H shrink ½, V shift up 1,H shift right π/2.
8-3 Trigonometry Part 2: Inverse Trigonometric Functions.
ANSWERS. Using Trig in every day life. Check Homework.
Section 7-6 The Inverse Trigonometric Functions. Inverse Trig. Functions With the trigonometric functions, we start with an angle, θ, and use one or more.
Copyright © by Holt, Rinehart and Winston. All Rights Reserved. Objective Evaluate trigonometric expressions involving inverses Inverses of Trigonometric.
Inverse Trig Functions Vocabulary Inverse Cosine Function (cos -1 ) – The function y=cos -1 x = Arccos x, if and only if x = cos y and 0 ≤ y ≤ π Inverse.
EXAMPLE 1 Use an inverse tangent to find an angle measure Use a calculator to approximate the measure of A to the nearest tenth of a degree. SOLUTION Because.
Trigonometric Functions
Inverse Trigonometric: Integration
Exponential Function Next slide © Annie Patton.
Chapter 1 Functions.
Use an addition or subtraction formula to find the exact value of the expression: {image} Select the correct answer: {image}
2005 Paper 1 No 7 © Annie Patton Next Slide.
Graphs 10 y 5 x © Annie Patton Next Slide.
Trigonometric Functions
Second Derivatives © Annie Patton Next slide.
Lesson 7-3 Trig Substitution.
General Rule © Annie Patton Next Slide.
Quotient Next Slide © Annie Patton.
Miscellaneous Differential Problems
x x HW 13: Inverse Trig Functions HW 13: Inverse Trig Functions
Presentation transcript:

© Annie Patton Differentiation of Inverse Trigonometric Function Next Slide

© Annie Patton Aim of Lesson To establish what an inverse trigonometric function is, then differentiate the inverse of sin and tan from first principles and use these formulas. Next Slide

© Annie Patton Inverse Trigonometric Function It is the inverse of sin. Next Slide

© Annie Patton a is a constant Next Slide This formula is given in the tables.

© Annie Patton Next Slide Start clicking when you want to see the answer.

© Annie Patton a is a constant Next Slide This formula is given in the tables.

© Annie Patton Differentiate of y=tan -1 4x Next Slide Start clicking when you want to see the answer.

© Annie Patton Leaving Certificate Higher No 6b(i) Paper Next Slide Start clicking when you want to see the answer.

© Annie Patton Leaving Certificate Higher No 7 b (1) Paper Next Slide Start clicking when you want to see the answer.

© Annie Patton Leaving Certificate Higher No 6c (i) Paper Next Slide Start clicking when you want to see the answer.

© Annie Patton Homework. Differentiate the following: Next Slide

© Annie Patton Conclusion Next Slide

© Annie Patton Conclusion Next Slide

© Annie Patton Note the differentiation of cos -1 is not on the syllabus.