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.

Slides:

Advertisements

Similar presentations

6.6 Trig Equations & Inequalities in Quadratic Form.

Advertisements

Trigonometric Identities

Trig Graphs. y = sin x y = cos x y = tan x y = sin x + 2.

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.

5.5 Solving Trigonometric Equations Example 1 A) Is a solution to ? B) Is a solution to cos x = sin 2x ?

5.8 Quadratic Inequalities

Solving Trigonometric Equations. First Degree Trigonometric Equations: These are equations where there is one kind of trig function in the equation and.

Section 5.5.  In the previous sections, we used: a) The Fundamental Identities a)Sin²x + Cos²x = 1 b) Sum & Difference Formulas a)Cos (u – v) = Cos u.

7.4.2 – Solving Trig Equations, Cont’d. Sometimes, we may have more than one trig function at play while trying to solve Like having two variables.

1 7.3 Evaluating Trig Functions of Acute Angles In this section, we will study the following topics: Evaluating trig functions of acute angles using right.

2.5 Properties of the Trig Functions

Verify a trigonometric identity

Approximating Zeroes Learning Objective: to be able to find all critical points of a polynomial function. Warm-up (IN) Describe the graph: 1. 2.

6.8 –Systems of Inequalities. Just like systems of equations, but do the inequality part!

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

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:///

Verify a trigonometric identity

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.

18 Days. Four days  We will be using fundamental trig identities from chapter 5 and algebraic manipulations to verify complex trig equations are in.

Standardized Test Practice

Trigonometric Equations Edited by Mr. Francis Hung Last Updated:

2.3 Computing the Values of Trig Functions of Acute Angles Warm-up (IN) Learning Objective: To compute values of common trig expressions, both by hand.

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.

6-2A Solving by Substitution Warm-up (IN) Learning Objective: to solve systems of equations using substitution Graph and solve the system of equations.

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:

3.6 Solving Absolute Value Equations and Inequalities

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

Sin, Cos, Tan with a calculator  If you are finding the sin, cos, tan of an angle that is not a special case (30, 60, 45) you can use your calculator.

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,

Evaluating Logs and Antilogs Warm-up Solve: Learning Objective: to evaluate and solve equations with logs of bases other than those we’re used to.

Chapter 5 Analytic Trigonometry Sum & Difference Formulas Objectives:  Use sum and difference formulas to evaluate trigonometric functions, verify.

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

1 8.7 Trigonometric Equations (I) In this section, we will study the following topics: o Solving equations involving a single trig function algebraically.

1.8 Absolute Value Equations and Inequalities Warm-up (IN) Learning Objective: to write, solve and graph absolute value in math and in real-life situations.

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,

5-2B Two-Point Equation of a Line Warm-up (IN) Learning Objective: to determine the equation of a line through 2 given points. Rewrite the equations in.

Aim: Solving Quadratic Trig Equations Course: Alg. 2 & Trig. Aim: How do we solve quadratic trigonometric equations? Do Now: Solve by factoring: x 2 –

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.

Warm-up 4-1. x – y = 33x + y = 52y = 6 – x x + y = 5x – 2y = 43x – 2y = 6 Graphs:

2.6 Graphing Sine and Cosine Functions Warm-up (IN) 1.Identify the transformations from to Learning Objective: To graph sine and cosine functions and to.

Aim: How do we solve trig equations using reciprocal or double angle identities? Do Now: 1. Rewrite in terms of 2. Use double angle formula to rewrite.

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,

1.2 Cont. Learning Objective: to continue to find terms of sequences and then to find the sum of a geometric series. Warm-up (IN) 1.Give the first 4 terms.

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.

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,

4.3 Right Triangle Trigonometry Objective: In this lesson you will learn how to evaluate trigonometric functions of acute angles and how to use the fundamental.

PreCalculus 89-R 8 – Solving Trig Equations 9 – Trig Identities and Proof Review Problems.

Double Angle Identities (1) sin (A + A) = sin A cos A + cos A sin A sin (2A) sin (2A) = 2 sin A cos A sin (A + B) = sin A cos B + cos A sin B What does.

C2 TRIGONOMETRY.

3.3 – Solving Systems of Inequalities by Graphing

6.5 Applications of Common Logarithms

Solving Trigonometric Equations

F(x) = x2 x > 3 Find the range of f(x) f(x) > 9.

SOLVING TRIG EQUATIONS

Find all solutions of the equation

Warm-up: HW: pg. 490(1 – 4, 7 – 16, , 45 – 48)

Examples Double Angle Formulas

5.1 Solving Systems of Equations by Graphing

Trig Graphs And equations Revision A2.

8.1 Graphical Solutions to Trig. Equations

Trig Graphs And equations Revision.

x x HW 13: Inverse Trig Functions HW 13: Inverse Trig Functions

Trigonometric Equations

Presentation transcript:

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 procedure to locate the solutions using appropriate visual cues, and develop number sense with extensive use of fractions.

Ex 1 – Determine whether the following are solutions to the equation No! Yes!

Ex 2 – Solve. List 8 solutions What is the period for cos? So… Ex 3 – Solve the equations on the interval General formula

We know where sin=1/2 So… But…there are more π/12s that work! So, use the general formula…

We know where tan=1 So…

Ex 4 – Solve using calculator We can use 2 nd sin, but that would only give us one answer and we need all of them between 0 and 2 π So, graph it…but don’t forget to change to radians! And, change your window

HW – 272 #7- 12,25,27,31,32,41- 43,53,54 Out – solve Summary – I think I understand… Don’t forget about POW!! Toys for Tots!