7-6 Solving Trigonometric Equations Finding what x equals.

Slides:



Advertisements
Similar presentations
Trigonometric Equations
Advertisements

Section 7.1 The Inverse Sine, Cosine, and Tangent Functions.
Trigonometric Identities
Get out paper for notes!!!.
The Inverse Trigonometric Functions Section 4.2. Objectives Find the exact value of expressions involving the inverse sine, cosine, and tangent functions.
7.4 Trigonometric Functions of General Angles
Solving Equations with the Variable on Both Sides Objectives: to solve equations with the variable on both sides.
The Trigonometric Functions What about angles greater than 90°? 180°? The trigonometric functions are defined in terms of a point on a terminal side r.
Trigonometric Equations Solve Equations Involving a Single Trig Function.
MTH 112 Elementary Functions Chapter 6 Trigonometric Identities, Inverse Functions, and Equations Section 1 Identities: Pythagorean and Sum and Difference.
Section 4 Inverses of the Trigonometric Functions
5.5 Solving Trigonometric Equations Example 1 A) Is a solution to ? B) Is a solution to cos x = sin 2x ?
Solving Trigonometric Equations
Solving Equations with the Variable on Both Sides
Sum and Difference Formulas Section 5.4. Exploration:  Are the following functions equal? a) Y = Cos (x + 2)b) Y = Cos x + Cos 2 How can we determine.
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.
5.3 Solving Trigonometric Equations. What are two values of x between 0 and When Cos x = ½ x = arccos ½.
8.5 Solving More Difficult Trig Equations
7.1 – Basic Trigonometric Identities and Equations
4.4 Trigonometric Functions of any Angle Objective: Students will know how to evaluate trigonometric functions of any angle, and use reference angles to.
Section 10.1 Polar Coordinates.
Lesson 7-2 Hard Trig Integrals. Strategies for Hard Trig Integrals ExpressionSubstitutionTrig Identity sin n x or cos n x, n is odd Keep one sin x or.
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.
10.4 Solve Trigonometric Equations
Vocabulary inequality algebraic inequality solution set 1-9 Introduction to Inequalities Course 3.
Sum and Difference Formulas New Identities. Cosine Formulas.
Section 6.1 Inverse Trig Functions Section 6.2 Trig Equations I Section 6.3 Trig Equations II Section 6.4 Equations Chapter 6 Inverse Trig Functions and.
Trigonometric Equations M 140 Precalculus V. J. Motto.
Section 7.5 Unit Circle Approach; Properties of the Trigonometric Functions.
5.3 Solving Trigonometric Equations
By Mr.Bullie. Trigonometry Trigonometry describes the relationship between the side lengths and the angle measures of a right triangle. Right triangles.
13.1 Trigonometric Identities
4.7 Inverse Trig Functions. By the end of today, we will learn about….. Inverse Sine Function Inverse Cosine and Tangent Functions Composing Trigonometric.
The Unit Circle M 140 Precalculus V. J. Motto. Remembering the “special” right triangles from geometry. The first one is formed by drawing the diagonal.
Section 1.4 Trigonometric Functions an ANY Angle Evaluate trig functions of any angle Use reference angles to evaluate trig functions.
Slide 9- 1 Copyright © 2006 Pearson Education, Inc. Publishing as Pearson Addison-Wesley.
1 Start Up Day 37 1.Simplify: 2, Verify:. SOLVING TRIGONOMETRIC EQUATIONS-DAY 37 OBJECTIVE : SWBAT SOLVE TRIGONOMETRIC EQUATIONS. EQ: How can we use trigonometric.
7-6 Solving Trigonometric Equations Finding what x equals.
1.6 Trigonometric Functions: The Unit circle
EXAMPLE 1 Evaluate trigonometric functions given a point Let (–4, 3) be a point on the terminal side of an angle θ in standard position. Evaluate the six.
5.3 Solving Trigonometric Equations
Trigonometric Functions Section 1.6. Radian Measure The radian measure of the angle ACB at the center of the unit circle equals the length of the arc.
Section 8-1 Simple Trigonometric Equations. Solving Trigonometric Equations The sine graph (on p. 295) illustrates that there are many solutions to the.
Warm UP Graph arcsin(x) and the limited version of sin(x) and give their t-charts, domain, and range.
DO NOW QUIZ Take 3 mins and review your Unit Circle.
Section 4.2 The Unit Circle. Has a radius of 1 Center at the origin Defined by the equations: a) b)
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.
Remember an identity is an equation that is true for all defined values of a variable. We are going to use the identities that we have already established.
Section 4.7 Inverse Trigonometric Functions. Helpful things to remember. If no horizontal line intersects the graph of a function more than once, the.
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.
Section 8-5 Solving More Difficult Trigonometric Functions.
Do Now  .
Analytic Trigonometry
7 Analytic Trigonometry
Copyright © 2014, 2010, 2007 Pearson Education, Inc.
Solving Trigonometric Equations
Analytic Trigonometry
18. More Solving Equations
THE UNIT CIRCLE SECTION 4.2.
Basic Trigonometric Identities and Equations
Trigonometric Functions: The Unit Circle (Section 4-2)
Unit 7B Review.
The Inverse Trigonometric Functions (Continued)
11. Solving Trig Equations
19. More Solving Equations
11. Solving Trig Equations
An Inverse Function What was that again?
The Circular Functions (The Unit Circle)
Presentation transcript:

7-6 Solving Trigonometric Equations Finding what x equals

It is just like solving regular equations, but once you get solutions, you have to find corresponding angle measure. Lets try a problem then see the rules.

What are the rules? 1.“x” means give the answer in __________; “Θ” means give the answer in ___________. 2.“Solve for 0 ≤ x < 2π” means give all the answers on one pass around the unit circle. 3.“General solution” means ______________ __________________________________ 4. Guess what: Work on both sides of the equation using all the rules of algebra. That is a) _____________ or b) ___________

Is that it? Well, yes, except for one footnote. Never Never Never Never divide both sides by the same trig function to get rid of it. For example, It will eliminate answers.

Lets Try a few

7-6 Solving Trigonometric Equations Day 2

Lets go back to the solutions from yesterday and turn them into general solutions. General Solutions will help you find every single solution no matter how many times around the circle All we do is add after the answers for one time around the circle. Or for tangent answers because ___________________________________ ___________________________________

General Solution

6-5 Inverse Trig An Inverse Function What was that again?

Lets remember: What is an inverse function? What is the notation? ___________________________ In a way, you have been practicing the inverse trig process. In section 7-6, you had the trig value and found the angle.

f(x) = sin xf(x) = sin -1 x What is the problem here? ______________________________

How do we take care of that? Therefore, there are limits on the answers that you can get. Use your calculator to find cos -1 (-.5) _____________________________

Each function has a limited Range For sin -1 x, csc -1 x, tan -1 x ____________________________ For cos -1 x, sec -1 x, cot -1 x ____________________________

REMEMBER With inverse trig you give only ___________ ___________________________________ An answer in quadrant 4 such as 300  must be given as -60 . BE Careful!!

A Hint To give yourself something to remember, use the phrase “What angle has a” for the symbol -1. SO, lets try some problems.

Inverse Rule

6-5 Day 2 Inverse Trig Continued

We will now combine Inverse Trig with: Addition and Subtraction Formulas Double Angle Formulas Half Angle Formulas

Example AB