QUADRANT I THE UNIT CIRCLE. REMEMBER Find the length of the missing side: 1 1 1 x y x y x y Aim: Use the unit circle in order to find the exact value.

Slides:



Advertisements
Similar presentations
SOHCAHTOA TOA CAH SOH The three trigonometric ratios for right angled triangles are considered here. Click on a box to select a ratio.
Advertisements

an input/output machine where…
Special Triangles: 45 o -45 o -90 o ° x x Example: 45° 7 7 x x.
1 7.2 Right Triangle Trigonometry In this section, we will study the following topics: Evaluating trig functions of acute angles using right triangles.
Honors Geometry Section 10.3 Trigonometry on the Unit Circle
Trigonometric Function Graphs. a A B C b c General Right Triangle General Trigonometric Ratios SOH CAH TOA.
Day 3 Notes. 1.4 Definition of the Trigonometric Functions OBJ:  Evaluate trigonometric expressions involving quadrantal angles OBJ:  Find the angle.
Trigonometry The Unit Circle.
Trigonometry/Precalculus ( R )
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.
Trigonometric Functions on the
Unit Circle Definition of Trig Functions. The Unit Circle  A unit circle is the circle with center at the origin and radius equal to 1 (one unit). 
UNIT CIRCLE. Review: Unit Circle – a circle drawn around the origin, with radius 1.
Terminal Arm Length and Special Case Triangles DAY 2.
Definition of Trigonometric Functions With trigonometric ratios of acute angles in triangles, we are limited to angles between 0 and 90 degrees. We now.
Using Trigonometric Ratios
Trigonometric Functions
Geometry Notes Lesson 5.3A – Trigonometry T.2.G.6 Use trigonometric ratios (sine, cosine, tangent) to determine lengths of sides and measures of angles.
Trigonometry. Basic Ratios Find the missing Law of Sines Law of Cosines Special right triangles
TRIG FUNCTIONS OF ACUTE ANGLES Section 12-2 Pages
9.5 Trigonometric Ratios Sin-Cos-Tan. What is Trigonometry? Trigonometry (from Greek trigōnon "triangle" + metron "measure") is a branch of mathematics.
9.5 Trigonometric ratios How are trigonometric ratios used to find missing sides of right triangles?
Table of Contents 5. Right Triangle Trigonometry
13.2 – Define General Angles and Use Radian Measure.
4.2 Day 1 Trigonometric Functions on the Unit Circle Pg. 472 # 6-10 evens, evens, 46, 54, 56, 60 For each question (except the 0 o, 90 o, 180 o,
30º 60º 1 45º 1 30º 60º 1 Do Now: Find the lengths of the legs of each triangle.
1 © 2010 Pearson Education, Inc. All rights reserved © 2010 Pearson Education, Inc. All rights reserved Chapter 4 Trigonometric Functions.
Introduction to the Unit Circle in Trigonometry. What is the Unit Circle? Definition: A unit circle is a circle that has a radius of 1. Typically, especially.
TANGENT THE UNIT CIRCLE. REMEMBER Find x in the right triangle above. x 1 30° Find y in the right triangle below. y Using your calculator, what is the.
TRIGONOMETRIC RATIOS Chapter 9.5. New Vocabulary  Trigonometric Ratio: The ratio of the lengths of two sides or a right triangle.  The three basic trigonometric.
Copyright © 2011 Pearson, Inc. 4.3 Trigonometry Extended: The Circular Functions Goals: Solve problems involving trigonometric functions. Memorize the.
Using Fundamental Identities To Find Exact Values. Given certain trigonometric function values, we can find the other basic function values using reference.
13.1 – Use Trig with Right Triangles
Evaluating Trigonometric Functions (Precalculus Review 3) September 10th, 2015.
Review: Special Right Triangles 30 o 60 o 45 o 13-2 Angles & the Unit Circle Day 1 Today’s Objective: I can work with angles in standard position.
Review of Trig Ratios 1. Review Triangle Key Terms A right triangle is any triangle with a right angle The longest and diagonal side is the hypotenuse.
Properties of the Trigonometric Functions
Table of Contents 3. Right Triangle Trigonometry.
Angles and the Unit Circle. An angle is in standard position when: 1) The vertex is at the origin. 2) One leg is on the positive x – axis. (This is the.
Right Triangles Consider the following right triangle.
8.4 Trigonometric Ratios.
Lesson 13.1 Right Triangle Trigonometry
7.5 & 7.6– Apply the Sin-Cos-Tan Ratios. Hypotenuse: Opposite side: Adjacent side: Side opposite the reference angle Side opposite the right angle Side.
Trigonometric Functions. A Block Data B Block Data.
1 7.2 Right Triangle Trigonometry In this section, we will study the following topics: Evaluating trig functions of acute angles using right triangles.
Unit 7: Right Triangle Trigonometry
Trigonometric Functions: The Unit Circle Section 4.2.
Right Triangle Trigonometry Ratios Must label the sides B A C From the marked angle… Hypotenuse- across from the right angle Adjacent – next to.
Chapter 13 Right Angle Trigonometry
Splash Screen. Then/Now You used the Pythagorean Theorem to find missing lengths in right triangles. Find trigonometric ratios using right triangles.
Angles & the Unit Circle Day 1 Today’s Objective: I can work with angles in standard position.
Trigonometry Section 7.3 Define the sine and cosine functions Note: The value of the sine and cosine functions depend upon the quadrant in which the terminal.
14.1 The Unit Circle Part 2. When measuring in radians, we are finding a distance ____ the circle. This is called. What is the distance around a circle?
 Find the value of the other five trigonometric functions.
Bell Work R Find the 6 trig functions for
Objective: Use unit circle to define trigonometric functions. Even and odd trig functions. Warm up 1.Find and. 2.Give the center and radius of a circle.
Definition 3: Trigonometric Functions: The Unit Circle 3.4 JMerrill, 2009 Contributions from DDillon.
Unit 3 Trigonometry Review Radian Measure Special Angles Unit Circle 1.
Right Triangle Trigonometry
The unit circle.
8-4 Trigonometry Ms. Andrejko.
Objectives Find the sine, cosine, and tangent of an acute angle.
What are Reference Angles?
The Trigonometric Ratios
A 5 4 C 3 B 3 5 Sin A =.
LESSON ____ SECTION 4.2 The Unit Circle.
Unit 3: Right Triangle Trigonometry
Trigonometry 2 L.O. All pupils can find missing sides on right angled triangles All pupils can find missing angles in right angled triangles.
10-6 Trigonometric Ratios
5.2 Apply the Tangent Ratio
Presentation transcript:

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 of a trigonometric expression.

THE UNIT CIRCLE Draw a circle whose center at the origin, (0, 0), and has a radius of Aim: Use the unit circle in order to find the exact value of a trigonometric expression.

QUADRANT I 30° (, ) 1 45° (, ) 1 60° (, ) 1 1 Aim: Use the unit circle in order to find the exact value of a trigonometric expression. Place Special Triangles into the first quadrant of the Unit Circle then label the points created.

Soh Cah Toa: Aim: Use the unit circle in order to find the exact value of a trigonometric expression.

CRITICAL ANGLE TABLE 0°30°45°60°90° Sin Cos Tan Aim: Use the unit circle in order to find the exact value of a trigonometric expression.

EXACT VALUE The drawing of the Unit Circle (first quadrant) or the table just created can be used to find the exact value of the following trigonometric expression: Find the exact value of Aim: Use the unit circle in order to find the exact value of a trigonometric expression.