3.2 The Inverses Continued Warm-up (IN) 1.What is the domain and range of ? 2.True or False: The graph of is increasing on the interval and. 3. If and,

Slides:

Advertisements

Similar presentations

Trigonometric Identities

Advertisements

The Inverse Trigonometric Functions Section 4.2. Objectives Find the exact value of expressions involving the inverse sine, cosine, and tangent functions.

Evaluating Sine & Cosine and and Tangent (Section 7.4)

3.1 The inverse sine, cosine, and tangent functions Warm-up (IN) 1.What is the domain and range of ? 2.True or False: The graph of is decreasing on the.

3.8 Trig Equations (cont.) Warm-up (IN) 1.Solve: Learning Objective: to continue to learn techniques that are useful in solving trig identities, including.

Review of Trigonometry

Day 2 and Day 3 notes. 1.4 Definition of the Trigonometric Functions OBJ:  Evaluate trigonometric expressions involving quadrantal angles OBJ:  Find.

Pg. 346/352 Homework Pg. 352 #6, 8 – 11, 15 – 17, 21, 22, 24, 27, 28, 30 – 32.

1.5 Using the Definitions of the Trigonometric Functions OBJ: Give the signs of the six trigonometric functions for a given angle OBJ: Identify the quadrant.

Section 5.2 Trigonometric Functions of Real Numbers Objectives: Compute trig functions given the terminal point of a real number. State and apply the reciprocal.

TRIGONOMETRY. Sign for sin , cos  and tan  Quadrant I 0° <  < 90° Quadrant II 90 ° <  < 180° Quadrant III 180° <  < 270° Quadrant IV 270 ° < 

7.3 Trigonometric Functions of Angles. Angle in Standard Position Distance r from ( x, y ) to origin always (+) r ( x, y ) x y  y x.

Properties of the Trigonometric Functions. Domain and Range Remember: Remember:

5.3 S OLVING T RIG EQUATIONS. S OLVING T RIG E QUATIONS Solve the following equation for x: Sin x = ½.

4.6 Other Inverse Trig Functions. To get the graphs of the other inverse trig functions we make similar efforts we did to get inverse sine & cosine. We.

2.5 Properties of the Trig Functions

10.4A Polar Equations Rectangular: P (x, y) Polar: P (r,  )  r = radius (distance from origin)   = angle (radians)

4.6 Graphs of Other Trigonometric Functions Objectives –Understand the graph of y = tan x –Graph variations of y = tan x –Understand the graph of y = cot.

1.2 Domain of Functions Mon Sept 15 Do Now Find the domain of each function 1) 2)

Find the reference angle

WARM-UP Prove: sin 2 x + cos 2 x = 1 This is one of 3 Pythagorean Identities that we will be using in Ch. 11. The other 2 are: 1 + tan 2 x = sec 2 x 1.

Section 6.4 Inverse Trigonometric Functions & Right Triangles

6-1B Solving Linear Systems by Graphing Warm-up (IN) Learning Objective: to solve a system of 2 linear equations graphically Given the equations: 1.Which.

2.1 Review of Functions Learning Objective: to remember what a function is and what to do with it. Warm-up (IN) 1.Write down everything you think of when.

Section 4.2 Trigonometric Functions: The Unit Circle

Sec 6.2 Trigonometry of Right Triangles Objectives: To define and use the six trigonometric functions as ratios of sides of right triangles. To review.

Slide Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley.

Section 7.5 Unit Circle Approach; Properties of the Trigonometric Functions.

4.2 Trigonometric Functions (part 2) III. Trigonometric Functions. A) Basic trig functions: sine, cosine, tangent. B) Trig functions on the unit circle:

Advanced Precalculus Notes 5.3 Properties of the Trigonometric Functions Find the period, domain and range of each function: a) _____________________________________.

3.4 Sum and Difference Formula Warm-up (IN) 1.Find the distance between the points (2,-3) and (5,1). 2.If and is in quad. II, then 3.a. b. Learning Objective:

Flashback Which of the following expressions is the closest approximation to the height h, in feet, of the roof truss shown below? A. 15 tan 20°

Trig Review. 1.Sketch the graph of f(x) = e x. 2.Sketch the graph of g(x) = ln x.

3.7 Trig Equations Warm-up (IN) 1.Solve: 2.Find the exact value of: Learning Objective: to identify numerous solutions to trig equations, understand the.

Reciprocal functions secant, cosecant, cotangent Secant is the reciprocal of cosine. Reciprocal means to flip the ratio. Cosecant is the reciprocal of.

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

2.6 Cont. Warm-up (IN) 1.Identify the transformations from to 2.Graph Learning Objective: To be able to identify the amplitude, period, 4 sub- intervals,

Inverse Functions Notes 3.8. I. Inverse Functions A.) B.) Ex. –

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)

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.

Pg. 407/423 Homework Pg. 407#33 Pg. 423 #16 – 18 all #19 Ѳ = kπ#21t = kπ, kπ #23 x = π/2 + 2kπ#25x = π/6 + 2kπ, 5π/6 + 2kπ #27 x = ±1.05.

3.6 Product-to-Sum and Sum-to- Product Formulas Warm-up (IN) 1.Find the exact value of: Learning Objective: To be able to properly identify which product-to-sum.

2.8 Phase Shift and Sinusoidal Curve Fitting Warm-up (IN) - none Learning Objective: To graph sinusoidal functions of the form using the amplitude, period,

Section 7.3 Double-Angle, Half-Angle and Product-Sum Formulas Objectives: To understand and apply the double- angle formula. To understand and apply the.

Important Angles.

2.5 Inverses Warm-up (IN) Learning Objective: to find the inverse of a relation or function and to determine whether the inverse of a function is a function.

6.1 – 6.5 Review!! Graph the following. State the important information. y = -3csc (2x) y = -cos (x + π/2) Solve for the following: sin x = 0.32 on [0,

A. Calculate the value of each to 4 decimal places: i)sin 43sin 137sin 223sin 317. ii) cos 25cos 155cos 205cos 335. iii)tan 71tan 109 tan 251tan 289.

Math III Accelerated Chapter 14 Trigonometric Graphs, Identities, and Equations 1.

C H. 4 – T RIGONOMETRIC F UNCTIONS 4.4 – Trig Functions of Any Angle.

MULTIPLE ANGLE & PRODUCT –TO-SUM IDENTITIES Section 5-5.

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

The Unit Circle and Circular Functions Trigonometry Section 3.3.

Trigonometric Identities and Equations

Warm Up Use trigonometric identities to simplify: csc ∙tan

Lesson 4.7 Inverse Trigonometric Functions

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

Using Fundamental Identities

Warm-up: 1) Make a quick sketch of each relation

Graphing Tangent and the Reciprocal Functions

Solving Trigonometric Equations (Section 5-3)

2) Find one positive and one negative coterminal angle to

The Inverse Trigonometric Functions (Continued)

Multiple-Angle and Product-to-Sum Formulas (Section 5-5)

Math /4.4 – Graphs of the Secant, Cosecant, Tangent, and Cotangent Functions.

FUNCTIONS & THEIR GRAPHS

Given A unit circle with radius = 1, center point at (0,0)

Presentation transcript:

3.2 The Inverses Continued Warm-up (IN) 1.What is the domain and range of ? 2.True or False: The graph of is increasing on the interval and. 3. If and, then ____? Learning Objective: To identify and understand the procedure of solving more involved inverse expressions, to understand the limitations of cot, csc, and sec inverse functions, and to be able to use the calculator to check your work. D: all real #s except odd multiples of R: True

NOTES Ex 1 – Find the exact value of…

where is sin neg? Quad III & IV must be in IV where is cos neg? Quad II & III must be in II

Limits to inverses: X (values) Y (angles) Except 0 Except

Find the exact value of Ex 2 - Approximate the value of each... Ex 3 -

Cot and tan don’t have the same range, so we can’t use tan… What has the same range as cot?? Cos! So…we need to find out what cos is…

HW – pg. 236 #9-16,21-26,33-35,39-43 Out – Find Summary – I think working with inverses can be difficult because… Don’t forget about POW!!