Right Triangle Trig Review Given the right triangle from the origin to the point (x, y) with the angle, we can find the following trig functions:

Slides:

Advertisements

Similar presentations

Trigonometric Equations

Advertisements

Trig for M2 © Christine Crisp.

Copyright © 2013, 2009, 2005 Pearson Education, Inc. 1 5 Trigonometric Identities.

Sum and Difference Identities for Sine and Tangent

1.3 Use Midpoint and Distance Formulas

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 and establish.

Chapter 7 Trigonometric Identities and Equations.

Section 8.4: Trig Identities & Equations

The Unit Circle.

14-5 Sum and Difference of Angles Formulas. The Formulas.

QUADRANT I THE UNIT CIRCLE. REMEMBER Find the length of the missing side: x y x y x y Aim: Use the unit circle in order to find the exact value.

In these sections, we will study the following topics:

MTH 112 Elementary Functions Chapter 6 Trigonometric Identities, Inverse Functions, and Equations Section 1 Identities: Pythagorean and Sum and Difference.

4.2, 4.4 – The Unit Circle, Trig Functions The unit circle is defined by the equation x 2 + y 2 = 1. It has its center at the origin and radius 1. (0,

Terminal Arm Length and Special Case Triangles DAY 2.

The Pythagorean Theorem and Its Converse

10.3 Verify Trigonometric Identities

EXAMPLE 1 Find trigonometric values Given that sin  = and <  < π, find the values of the other five trigonometric functions of . 4 5 π 2.

Tips For Learning Trig Rules. Reciprocal Rules Learn:

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.

Right Triangle Trig Review Given the right triangle from the origin to the point (x, y) with the angle, we can find the following trig functions:

P.5 Trigonometric Function.. A ray, or half-line, is that portion of a line that starts at a point V on the line and extends indefinitely in one direction.

4.3 Right Triangle Trigonometry Pg. 484 # 6-16 (even), (even), (even) –Use right triangles to evaluate trigonometric functions –Find function.

CHAPTER 7: Trigonometric Identities, Inverse Functions, and Equations

12-2 Trigonometric Functions of Acute Angles

Right Triangle Trigonometry

Identities The set of real numbers for which an equation is defined is called the domain of the equation. If an equation is true for all values in its.

Chapter 6 Trig 1060.

5.6 Angles and Radians (#1,2(a,c,e),5,7,15,17,21) 10/5/20151.

Sum and Difference Identities for Cosine. Is this an identity? Remember an identity means the equation is true for every value of the variable for which.

TRIG FUNCTIONS OF ACUTE ANGLES Section 12-2 Pages

Angle Identities. θsin θcos θtan θ 0010 –π/6–1/2√3/2–√3/3 –π/4–√2/2√2/2–1 –π/3–√3/21/2–√3 –π/2–10Undef –2π/3–√3/2–1/2√3 –3π/4–√2/2 1 –5π/6–1/2–√3/2√3/3.

November 5, 2012 Using Fundamental Identities

Sum and Difference Formulas New Identities. Cosine Formulas.

Pre-Calculus. Learning Targets Review Reciprocal Trig Relationships Explain the relationship of trig functions with positive and negative angles Explain.

Key Concept 1. Example 1 Evaluate Expressions Involving Double Angles If on the interval, find sin 2θ, cos 2θ, and tan 2θ. Since on the interval, one.

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.

Lesson 4.2. A circle with center at (0, 0) and radius 1 is called a unit circle. The equation of this circle would be (1,0) (0,1) (0,-1) (-1,0)

Lesson 4.2. A circle with center at (0, 0) and radius 1 is called a unit circle. The equation of this circle would be (1,0) (0,1) (0,-1) (-1,0)

1 © 2010 Pearson Education, Inc. All rights reserved © 2010 Pearson Education, Inc. All rights reserved Chapter 5 Analytic Trigonometry.

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

Vocabulary reduction identity. Key Concept 1 Example 1 Evaluate a Trigonometric Expression A. Find the exact value of cos 75°. 30° + 45° = 75° Cosine.

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

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

13.1 Trigonometric Identities

Trigonometric Identities

Slide Fundamental Identities 5.2 Verifying Trigonometric Identities 5.3 Sum and Difference Identities for Cosine 5.4 Sum and Difference Identities.

Right Triangles Consider the following right triangle.

Vocabulary identity trigonometric identity cofunction odd-even identities BELLRINGER: Define each word in your notebook.

Warm-Up 2/12 Evaluate – this is unit circle stuff, draw your triangle.

DO NOW QUIZ Take 3 mins and review your Unit Circle.

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.

Section 4.2 The Unit Circle. Has a radius of 1 Center at the origin Defined by the equations: a) b)

Area of Regular Polygons Terms Radius – segment joining the center of the polygon to the vertex of the polygon. All radii of a polygon are equal. When.

Trigonometry Section 8.4 Simplify trigonometric expressions Reciprocal Relationships sin Θ = cos Θ = tan Θ = csc Θ = sec Θ = cot Θ = Ratio Relationships.

Pythagorean Identities Unit 5F Day 2. Do Now Simplify the trigonometric expression: cot θ sin θ.

Then/Now You used sum and difference identities. (Lesson 5-4) Use double-angle, power-reducing, and half-angle identities to evaluate trigonometric expressions.

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

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.

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.

Definition 3: Trigonometric Functions: The Unit Circle 3.4 JMerrill, 2009 Contributions from DDillon.

TRIGONOMETRIC IDENTITIES

Copyright © 2017, 2013, 2009 Pearson Education, Inc.

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

5-3 Tangent of Sums & Differences

9.2: Sum and Differences of Trig Functions

Sum and Differences Section 5.3 Precalculus PreAP/Dual, Revised ©2017

What is coming up due?.

7.3 Sum and Difference Identities

Presentation transcript:

Right Triangle Trig Review Given the right triangle from the origin to the point (x, y) with the angle, we can find the following trig functions:

Replacing (x, y) with these new values, we get the point as: Moving to the circle centered at the origin

Moving to the circle centered at the origin with radius “r”, we find two points A and B.

We can use the distance formula to find the distance AB.

Next, construct the angle in a circle with the same radius r. Using the SAS property, the triangle AOB in the previous example is congruent to the triangle COD in this example. Therefore, the length of segment AB must equal the length of segment CD. It must also be true that 

Finding points C and D and the length CD, we get:

By similar triangles, we know the length of AB = length of CD. We can square both sides to get rid of the square roots.

Simplifying by squaring each group, we get: Every term has an r 2. Divide each term by r 2. Using the pythagorean identity, we know cos 2  cos  sin 2  cos 2  cos  cos  + cos 2  + sin   2sin  sin  + sin 2 

Simplifying, we get: Subtracting the 2’s from each side, we get: Each term has a -2, so divide out the -2.

However, recall that Replacing in the equation, we get:

To find a rule for, we replace  with  Simplifying with odd/even rules, we get:

To get the sum/difference rules for sin, we will use the co-function rule. Let’s use the cosine rule to find Using the cosine sum rule Using the co-function rules, we get:

Therefore: To get the sin   rule, Using the odd/even functions, we get:

Recall that tan  = (sin  cos , therefore… tan  = …….

Find the exact value of the following: a. cos (7  b. sin (17  c. cot (-15  )

1. sin (-  12) 2. tan (105  )

Find the exact value of each expression a. cos 70  cos20  - sin 70  sin20  b. sin(  12) cos(7  12) – sin(7  12)cos(  12)

Find the exact value of the expression:

Begin 8.4 p. 634 #9, 12, 15, 18, 21, 24, 26, 29, 30, 63, 67, 72, 75, 81 Cross out #41, 43, and 84 We will complete the rest tomorrow!! Daily quiz tomorrow at end of block over 8.4!

Given: a. Find cos (  b. Find sin(  c. Find tan ( 

Establish the identity: