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.

Slides:

Advertisements

Similar presentations

Trigonometric Identities

Advertisements

10.3 Double Angle and Half Angle Formulas

Trig – Section 4 Graphing Sine and Cosine Objectives: To graph sine and cosine curves To find amplitude, period and phase shifts.

Chapter 7 Trigonometric Identities and Equations.

Aim: What is the transformation of trig functions? Do Now: HW: Handout Graph: y = 2 sin x and y = 2 sin x + 1, 0 ≤ x ≤ 2π on the same set of axes.

In these sections, we will study the following topics:

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.

Verify a trigonometric identity

Verify a trigonometric identity

Aim: How do we sketch y = A(sin Bx) and

Trig – 4/21/2017 Simplify. 312 Homework: p382 VC, 1-8, odds

Section 5.5 Double Angle Formulas

Warm Up Sign Up. AccPreCalc Lesson 27 Essential Question: How are trigonometric equations solved? Standards: Prove and apply trigonometric identities.

5.1 Using Fundamental Identities

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

Sum and Difference Formulas New Identities. Cosine Formulas.

7.3 Sum and Difference Identities

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:

Using Trig Formulas In these sections, we will study the following topics: o Using the sum and difference formulas to evaluate trigonometric.

4.7 Inverse Trig Functions. By the end of today, we will learn about….. Inverse Sine Function Inverse Cosine and Tangent Functions Composing Trigonometric.

Further Trigonometric identities and their applications.

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

Solving Trigonometric Equations T, 11.0: Students demonstrate an understanding of half-angle and double- angle formulas for sines and cosines and can use.

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

Aim: How do we solve first and second degree trig equation? Do Now: 1. Solve for x: 6x + 7 = Given the equation 6sin x + 7 = 10 find : a) sin x.

5.5 Double Angle Formulas I. Double Angle Formulas. A) B) C)

6.2 Solving Trigonometric Equations with Identities.

MATHPOWER TM 12, WESTERN EDITION Chapter 5 Trigonometric Equations.

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.

Warm-Up Write the sin, cos, and tan of angle A. A BC

T.3.3 – Trigonometric Identities – Double Angle Formulas

Section 7-3 The Sine and Cosine Functions Objective: To use the definition of sine and cosine to find values of these functions and to solve simple trigonometric.

March 12, 2012 At the end of today, you will be able to use the double and half angle formulas to evaluate trig identities. Warm-up: Use the sum identities.

Warm-Up Get out lesson 22 CFU/ Hwk Complete problems 1-11 on the CFU.

Aim: What are the identities of sin (A ± B) and tan (A ±B)? Do Now: Write the cofunctions of the following 1. sin 30  2. sin A  3. sin (A + B)  sin.

5-4 Multiple-Angle Identities. Trig Identities Song To the tune of Rudolph the Red-Nosed Reindeer You know reciprocal and quotient and cofunction and.

Pg. 407/423 Homework Pg. 407#33 Pg. 423 #16 – 18 all #9 tan x#31#32 #1x = 0.30, 2.84#2x = 0.72, 5.56 #3x = 0.98#4No Solution! #5x = π/6, 5π/6#6Ɵ = π/8.

Sum and Difference Formulas. WARM-UP The expressions sin (A + B) and cos (A + B) occur frequently enough in math that it is necessary to find expressions.

Chapter 5 Analytic Trigonometry Multiple Angle Formulas Objective:  Rewrite and evaluate trigonometric functions using:  multiple-angle formulas.

Bilborough College Maths - core 4 double angle formulae (Adrian)

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.

Circular Functions & Trig Identities 3: Trigonometric Identities

Trig Identities A B C c a b.

Ch 5.5: Multiple-Angle and Product-to-Sum Formulas

5.3 Solving Trigonometric Equations Use standard algebraic techniques like collecting like terms and factoring.

Simple Trig Equations Dr. Shildneck.

Double- And Half-Angle Formulas

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

5-3 Tangent of Sums & Differences

Equivalent Functions Composite Angles Exact Trig Ratios

Homework Log Fri 4/22 Lesson 8 – 4 Learning Objective:

DO NOW 14.6: Sum and Difference Formulas (PC 5.4)

Product-to-Sum and Sum-to-Product Formulas

Aim: What are the double angle and half angle trig identities?

Examples Double Angle Formulas

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

Trig Equations w/ Multiple Angles.

5.5-Multiple Angle Formulas

Academy Algebra II 14.7: (PC 5.5): Multiple-Angle and Product-Sum

Other Trigonometric Identities

Aim: How do we solve first and second degree trig equation?

WArmup Rewrite 240° in radians..

7.3 Sum and Difference Identities

Double Angle Identities

Double Angle Formulas I. Double Angle Formulas. A) B) C)

HW: p.488 # 4,6,8,13,14,15,16,20 Aim: How do we prove trig identities?

Precalculus PreAP/Dual, Revised ©2017 §5.5: Double Angles Identity

Sum and Difference Formulas (Section 5-4)

Aim: How do we solve trig equations using

Presentation transcript:

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 HW: p.541 # 4,5,7,8,10,12,14,15

Suppose we like to solve for in the interval of for To do this, we just do like proving trig identity, we first rewrite the equation in terms of sine or cosine function. (reject)

Suppose we like to solve for in the interval of for We first need to use double angle formula to rewrite into Factor cos θ

1. Solve for x in the interval for 2. Solve for x in the interval for cos 2x + sin x = 1 3. Solve for in the interval for (60 ,300 ,180  )