Section 7.5 Trigonometric Equations Objective: To solve linear and quadratic trigonometric...

12
Section 7.5 Trigonometric Equations Objective: •To solve linear and quadratic trigonometric equations.

Transcript of Section 7.5 Trigonometric Equations Objective: To solve linear and quadratic trigonometric...

Page 1: Section 7.5 Trigonometric Equations Objective: To solve linear and quadratic trigonometric equations.

Section 7.5Trigonometric Equations

Objective:•To solve linear and quadratic trigonometric equations.

Page 2: Section 7.5 Trigonometric Equations Objective: To solve linear and quadratic trigonometric equations.

A trigonometric equation is an equation that contains a trigonometric function. For example:

To solve a trig equation, we use algebra to isolate the trig function on one side of the = sign.

2 2sin cos 1x x 2sin 1 0x 2tan 1 0x

Page 3: Section 7.5 Trigonometric Equations Objective: To solve linear and quadratic trigonometric equations.

Ex 1. Find all solutions to : 2sin 1 0x

Page 4: Section 7.5 Trigonometric Equations Objective: To solve linear and quadratic trigonometric equations.

Ex 2. Find all solutions to 2cos 2cos 1 0x x

Page 5: Section 7.5 Trigonometric Equations Objective: To solve linear and quadratic trigonometric equations.

Class Work

Find all solutions to the following:

1.

2.

sin 1 0x

2 cos 1 0x

Page 6: Section 7.5 Trigonometric Equations Objective: To solve linear and quadratic trigonometric equations.

Ex 3. Find all solutions to: 1 tan 0x

Page 7: Section 7.5 Trigonometric Equations Objective: To solve linear and quadratic trigonometric equations.

Ex 4. Find all solutions to: 3 tan 1 0x

Page 8: Section 7.5 Trigonometric Equations Objective: To solve linear and quadratic trigonometric equations.

Class Work

Find all solutions to the following:3.

4.

2tan 3 0x

21 tan 0x

Page 9: Section 7.5 Trigonometric Equations Objective: To solve linear and quadratic trigonometric equations.

Ex 5. Find all solutions to 2sec 2 0x

Page 10: Section 7.5 Trigonometric Equations Objective: To solve linear and quadratic trigonometric equations.

Ex 6 Find all solutions to sec 2cos 2 0x x

Page 11: Section 7.5 Trigonometric Equations Objective: To solve linear and quadratic trigonometric equations.

Class Work

Find all solutions to the following:

5.

6.

2csc 4x

2cos 3 2sin 1 0x x

Page 12: Section 7.5 Trigonometric Equations Objective: To solve linear and quadratic trigonometric equations.

HW p568 1-21 odd


Graph quadratic equations. Complete the square to graph quadratic equations. Use the Vertex Formula to graph quadratic equations. Solve a Quadratic Equation.

Graph quadratic equations. Complete the square to graph quadratic equations. Use the Vertex Formula to graph quadratic equations. Solve a Quadratic Equation.

Quadratic Equations - intranet.cesc.vic.edu.au Maths... · Topic 8 - Using quadratic equations to solve problems Chapter 2: Quadratic equations 17 Quadratic equations UNIT 8: Using

Quadratic Equations - intranet.cesc.vic.edu.au Maths... · Topic 8 - Using quadratic equations to solve problems Chapter 2: Quadratic equations 17 Quadratic equations UNIT 8: Using

SECTION 1.5 Quadratic Equations - MR. THOMPSON · Section 1.5 Quadratic Equations 147 Solving Quadratic Equations by the Square Root Property Quadratic equations of the form u2 =

SECTION 1.5 Quadratic Equations - MR. THOMPSON · Section 1.5 Quadratic Equations 147 Solving Quadratic Equations by the Square Root Property Quadratic equations of the form u2 =

Trigonometric Equations OBJECTIVES: Use standard algebraic techniques to solve trigonometric equations Solve trigonometric equations of quadratic type.

Trigonometric Equations OBJECTIVES: Use standard algebraic techniques to solve trigonometric equations Solve trigonometric equations of quadratic type.

A Univariate Rational Quadratic Trigonometric ...

A Univariate Rational Quadratic Trigonometric ...

In this section, you will learn to: Use standard algebraic techniques to solve trigonometric equations Solve trigonometric equations of quadratic type.

In this section, you will learn to: Use standard algebraic techniques to solve trigonometric equations Solve trigonometric equations of quadratic type.

3 Quadratic Equations and Complex Numbers · Solve quadratic equations by graphing. Solve quadratic equations algebraically. Solve real-life problems. Solving Quadratic Equations

3 Quadratic Equations and Complex Numbers · Solve quadratic equations by graphing. Solve quadratic equations algebraically. Solve real-life problems. Solving Quadratic Equations

Quadratic Equations Solving Quadratic Equations. 7/9/2013 Quadratic Equations 2 Solving Quadratic Equations Standard Form a x 2 + b x + c = 0 with a ≠

Quadratic Equations Solving Quadratic Equations. 7/9/2013 Quadratic Equations 2 Solving Quadratic Equations Standard Form a x 2 + b x + c = 0 with a ≠

8-5 Solving Quadratic Equations by Graphing · Solving Quadratic Equations by Graphing Objective Solve quadratic equations by graphing. Vocabulary quadratic equation Every quadratic

8-5 Solving Quadratic Equations by Graphing · Solving Quadratic Equations by Graphing Objective Solve quadratic equations by graphing. Vocabulary quadratic equation Every quadratic

5.3 Solving Trigonometric Equations *use standard algebraic techniques to solve trig equations *solve trig equations in quadratic form *solve trig equations.

5.3 Solving Trigonometric Equations *use standard algebraic techniques to solve trig equations *solve trig equations in quadratic form *solve trig equations.

8-1 Simple Trigonometric Equations - · PDF file08.11.2014 · 8-1 Simple Trigonometric Equations Objective: To solve simple Trigonometric Equations and apply them

8-1 Simple Trigonometric Equations - · PDF file08.11.2014 · 8-1 Simple Trigonometric Equations Objective: To solve simple Trigonometric Equations and apply them

09. Trigonometric Equations-1

09. Trigonometric Equations-1

TRIGONOMETRIC EQUATIONS - Plainvie · Trigonometric Equations and the Graphing Calculator Just as we used the graphing calculator to approximate the irrational solutions of quadratic-linear

TRIGONOMETRIC EQUATIONS - Plainvie · Trigonometric Equations and the Graphing Calculator Just as we used the graphing calculator to approximate the irrational solutions of quadratic-linear

06 Trigonometric Equations

06 Trigonometric Equations

Trigonometric equations

Trigonometric equations

Slide 6-1 Equations 6.1 Solving Trigonometric Equations 6.2 More on Trigonometric Equations 6.3 Trigonometric Equations Involving Multiples Angles 6.4.

Slide 6-1 Equations 6.1 Solving Trigonometric Equations 6.2 More on Trigonometric Equations 6.3 Trigonometric Equations Involving Multiples Angles 6.4.

Quadratic equations

Quadratic equations

Unit III Quadratic Equations - WordPress.com · Unit III Quadratic Equations 1 Section 7.1 – Solving Quadratic Equations by Graphing Investigating Solutions to Quadratic Equations

Unit III Quadratic Equations - WordPress.com · Unit III Quadratic Equations 1 Section 7.1 – Solving Quadratic Equations by Graphing Investigating Solutions to Quadratic Equations

Section 1.5 Quadratic Equations. Solving Quadratic Equations by Factoring.

Section 1.5 Quadratic Equations. Solving Quadratic Equations by Factoring.

Solving Quadratic Equations – Quadratic Formula The following shows how to solve quadratic equations using the Quadratic Formula. A quadratic equation.

Solving Quadratic Equations – Quadratic Formula The following shows how to solve quadratic equations using the Quadratic Formula. A quadratic equation.