Copyright © by Holt, Rinehart and Winston. All Rights Reserved. Objectives Find coterminal and reference angles. Find the trigonometric function values.

Slides:

Advertisements

Similar presentations

Copyright © by Holt, Rinehart and Winston. All Rights Reserved. Objectives Identify and evaluate rational functions. Graph a rational function, find its.

Advertisements

Section 14-4 Right Triangles and Function Values.

Day 2 and Day 3 notes. 1.4 Definition of the Trigonometric Functions OBJ:  Evaluate trigonometric expressions involving quadrantal angles OBJ:  Find.

Day 3 Notes. 1.4 Definition of the Trigonometric Functions OBJ:  Evaluate trigonometric expressions involving quadrantal angles OBJ:  Find the angle.

Copyright © by Holt, Rinehart and Winston. All Rights Reserved. Objectives Identify parallel lines and perpendicular lines by comparing their slopes. Write.

1.5 Using the Definitions of the Trigonometric Functions OBJ: Give the signs of the six trigonometric functions for a given angle OBJ: Identify the quadrant.

Trigonometric Functions of Any Angles

Copyright © 2009 Pearson Addison-Wesley Trigonometric Functions.

Trig Functions of Special Angles

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.

*Special Angles 45° 60° 30° 30°, 45°, and 60° → common reference angles Memorize their trigonometric functions. Use the Pythagorean Theorem;

Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Section 6.3 Properties of the Trigonometric Functions.

By: Alvin Nguyen. Unit Circle Jeopardy ConversionsRotation AnglesReference Angles Trig FunctionsWord Problems

Trigonometry/Precalculus ( R )

13.3 Evaluating Trigonometric Functions

13.1 Assignment C – even answers 18. sin = 4/1334. B = 53 o cos = a = tan = b = cot = sec = 38. A = 34 o csc = 13/4 b = c =

Chapter 14 Day 5 Trig Functions of Any Angle.  We can also evaluate trig functions of an angle that contains a point that isn’t necessarily on the unit.

9.3 Evaluate Trigonometric Functions of Any Angle

7.3 Trigonometric Functions of Angles. Angle in Standard Position Distance r from ( x, y ) to origin always (+) r ( x, y ) x y  y x.

MTH 112 Elementary Functions Chapter 5 The Trigonometric Functions Section 3 – Trigonometric Functions of Any Angle.

Drill Calculate:.

Trigonometric Functions Let (x, y) be a point other then the origin on the terminal side of an angle  in standard position. The distance from.

Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Section 7.4 Trigonometric Functions of General Angles.

Circular Trigonometric Functions.

13.3 Trigonometric Functions of General Angles

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

Copyright © by Holt, Rinehart and Winston. All Rights Reserved. Objectives Recognize arithmetic sequences, and find the indicated term of an arithmetic.

5.3 Right-Triangle-Based Definitions of Trigonometric Functions

6.2: Right angle trigonometry

Copyright © by Holt, Rinehart and Winston. All Rights Reserved. Objectives 8.2 Laws of Exponents: Powers and Products Find the power of a power. Find the.

Copyright © by Holt, Rinehart and Winston. All Rights Reserved. Objectives Solve and graph a linear inequality in two variables. Use a linear inequality.

Copyright © by Holt, Rinehart and Winston. All Rights Reserved. Represent a real-world linear relationship in a table, graph, or equation. Identify linear.

Copyright © by Holt, Rinehart and Winston. All Rights Reserved. Objectives Compare real numbers. Simplify expressions involving opposites and absolute.

Copyright © by Holt, Rinehart and Winston. All Rights Reserved. Objectives Multiply and divide rational expressions. Simplify rational expressions, including.

1.4 Definition of the Trigonometric Functions OBJ:  Find the values of the six trigonometric functions of an angle in standard position.

10-2 Angles of Rotation Warm Up Lesson Presentation Lesson Quiz

Chapter 6 – Trigonometric Functions: Right Triangle Approach Trigonometric Functions of Angles.

Advanced Precalculus Notes 5.3 Properties of the Trigonometric Functions Find the period, domain and range of each function: a) _____________________________________.

13.1 Trigonometric Identities

Using Fundamental Identities To Find Exact Values. Given certain trigonometric function values, we can find the other basic function values using reference.

4.4 Trigonometric Functions of Any Angle

Trig/Precalculus Section 5.1 – 5.8 Pre-Test. For an angle in standard position, determine a coterminal angle that is between 0 o and 360 o. State the.

Copyright © by Holt, Rinehart and Winston. All Rights Reserved. Objective Use the law of cosines to solve triangles The Law of Cosines.

Section 1.4 Trigonometric Functions an ANY Angle Evaluate trig functions of any angle Use reference angles to evaluate trig functions.

Pg. 362 Homework Pg. 362#56 – 60 Pg. 335#29 – 44, 49, 50 Memorize all identities and angles, etc!! #40

13-2 Angles of Rotation Warm Up Lesson Presentation Lesson Quiz

Copyright © by Holt, Rinehart and Winston. All Rights Reserved. Objectives Simplify and evaluate expressions involving logarithms. Solve equations involving.

Copyright © by Holt, Rinehart and Winston. All Rights Reserved. Objectives Write and apply direct-variation equations. Write and solve proportions. 1.4.

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.

Copyright © by Holt, Rinehart and Winston. All Rights Reserved. Objectives Solve a rational equation or inequality by using algebra, a table, or a graph.

Section 7.4 Trigonometric Functions of General Angles Copyright © 2013 Pearson Education, Inc. All rights reserved.

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

Section 7.4 Trigonometric Functions of General Angles.

Pre-Calculus Unit #4: Day 3.  Coterminal angles are angles in standard position (angles with the initial side on the positive x-axis) that have a common.

Trigonometric Ratios of Any Angle

Copyright © by Holt, Rinehart and Winston. All Rights Reserved. Objective Evaluate trigonometric expressions involving inverses Inverses of Trigonometric.

Copyright © by Holt, Rinehart and Winston. All Rights Reserved. Objective Solve mathematical and real-world problems by using the law of sines The.

Then/Now You found values of trigonometric functions for acute angles using ratios in right triangles. (Lesson 4-1) Find values of trigonometric functions.

Copyright © by Holt, Rinehart and Winston. All Rights Reserved. Objectives Use the quadratic formula to find real roots of quadratic equations. Use the.

Copyright © by Holt, Rinehart and Winston. All Rights Reserved. Objectives Evaluate natural exponential and natural logarithmic functions. Model exponential.

TRIGONOMETRIC FUNCTIONS OF ANY ANGLE

Warm Up Use trigonometric identities to simplify: csc ∙tan

Evaluating Trigonometric Functions

Trigonometry Terms Radian and Degree Measure

Properties of Trig Fcts.

Find the exact values of the trigonometric functions {image} and {image}

Trigonometric Functions: Unit Circle Approach

Conversions, Angle Measures, Reference, Coterminal, Exact Values

5-3 The Unit Circle.

Presentation transcript:

Copyright © by Holt, Rinehart and Winston. All Rights Reserved. Objectives Find coterminal and reference angles. Find the trigonometric function values of angles in standard position Angles of Rotation

Copyright © by Holt, Rinehart and Winston. All Rights Reserved. Glossary Terms angle of rotation coterminal angle degree initial side negative measure positive measure reference angle standard position terminal side 13.2 Angles of Rotation

Copyright © by Holt, Rinehart and Winston. All Rights Reserved. Rules and Properties Trigonometric Functions of  13.2 Angles of Rotation r =  x 2 + y 2 sin  = y r cos  = x r tan  = y x, x  0

Copyright © by Holt, Rinehart and Winston. All Rights Reserved. Rules and Properties Trigonometric Functions of  13.2 Angles of Rotation r =  x 2 + y 2 csc  = r y sec  = r x cot  = x y, y  0, x  0

Copyright © by Holt, Rinehart and Winston. All Rights Reserved. Key Skills Find coterminal angles and reference angles Angles of Rotation Coterminal angles of 217º such that –360º <  < 360º are found as follows: 17º – 360º = –143º Because a 217º angle is in Quadrant III, so the reference angle is |180º – 217º| = 37º.

Copyright © by Holt, Rinehart and Winston. All Rights Reserved. Key Skills Find the trigonometric function values of angles in standard position Angles of Rotation terminal side in Q IV tan  = – 5 4

Copyright © by Holt, Rinehart and Winston. All Rights Reserved. Key Skills Find the trigonometric function values of angles in standard position Angles of Rotation Use the Pythagorean Theorem to find r:  (–5) 2 =  41 sin  = – 5  41 cos  = 4  41 5  = 4  = TOC