Trigonometric Functions: The Unit Circle (Section 4-2)

Slides:



Advertisements
Similar presentations
The Inverse Trigonometric Functions Section 4.2. Objectives Find the exact value of expressions involving the inverse sine, cosine, and tangent functions.
Advertisements

Evaluating Sine & Cosine and and Tangent (Section 7.4)
Section 5.2 Trigonometric Functions of Real Numbers Objectives: Compute trig functions given the terminal point of a real number. State and apply the reciprocal.
Trigonometry/Precalculus ( R )
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.
Pre calculus Problem of the Day Homework: p odds, odds, odds On the unit circle name all indicated angles by their first positive.
Find the reference angle
Section 4.2 Trigonometric Functions: The Unit Circle
Section 7.5 Unit Circle Approach; Properties of the Trigonometric Functions.
4.2 Trigonometric Functions (part 2) III. Trigonometric Functions. A) Basic trig functions: sine, cosine, tangent. B) Trig functions on the unit circle:
14.2 The Circular Functions
Chapter 5 – Trigonometric Functions: Unit Circle Approach Trigonometric Function of Real Numbers.
Section 1.4 Trigonometric Functions an ANY Angle Evaluate trig functions of any angle Use reference angles to evaluate trig functions.
Pre-Calc Book Section 5.2 Trigonometric Functions of Real Numbers
Trigonometry Section 4.2 Trigonometric Functions: The Unit Circle.
Section 4.2 The Unit Circle. Has a radius of 1 Center at the origin Defined by the equations: a) b)
4.4 Trig Functions of Any Angle Objectives: Evaluate trigonometric functions of any angle Use reference angles to evaluate trig functions.
Find the values of the six trigonometric functions for 300
Right Triangle Trigonometry
Trigonometric Functions:Unit Circle
Lesson Objective: Evaluate trig functions.
The Other Trigonometric Functions
Introduction to the Six Trigonometric Functions & the Unit Circle
Trigonometric Functions: The Unit Circle Section 4.2
Trigonometric Functions: The Unit Circle 4.2
Pre-Calc: 4.2: Trig functions: The unit circle
Evaluating Angles.
12-3 Trigonometric Functions of General Angles
What are Reference Angles?
Trigonometric Function: The Unit circle
Copyright © 2014, 2010, 2007 Pearson Education, Inc.
Lesson 4.4 Trigonometric Functions of Any Angle
Mrs. Volynskaya Pre-Calculus Chapter 4 Trigonometry
Trig Functions: the unit circle approach
LESSON ____ SECTION 4.2 The Unit Circle.
Define General Angles and Radian Measure
Right Triangle Ratios Chapter 6.
Trigonometric Functions of Any Angle (Section 4-4)
Unit 7B Review.
Warm-Up: February 3/4, 2016 Consider θ =60˚ Convert θ into radians
Using Fundamental Identities
Warm-Up: Give the exact values of the following
Do Now Find the measure of the supplement for each given angle.
Objectives Students will learn how to use special right triangles to find the radian and degrees.
Right Triangle Ratios Chapter 6.
4.4 Trig Functions of any Angle
Properties of Trig Fcts.
2) Find one positive and one negative coterminal angle to
The Inverse Trigonometric Functions (Continued)
Introduction to College Algebra & Trigonometry
Multiple-Angle and Product-to-Sum Formulas (Section 5-5)
Warm Up 30°±
Trigonometric Functions: The Unit Circle
13-2 Angles of Rotation Warm Up Lesson Presentation Lesson Quiz
Trigonometric Functions: Unit Circle Approach
Trig. Ratios in a Coordinate System
Evaluating Angles.
Trigonometric Functions: The Unit Circle 4.2
Circular Trigonometric Functions.
Build and Use Unit Circle
6.4 - Trig Ratios in the Coordinate Plane
DAY 61 AGENDA: DG minutes.
5-4: Trig Identities Name:_________________ Hour: ________
5.2(c) Notes: A Bit of Calculus in Verifying Trig Identities
Review for test Front side ( Side with name) : Odds only Back side: 1-17 odd, and 27.
Academy Algebra II THE UNIT CIRCLE.
5-3 The Unit Circle.
Sum and Difference Formulas (Section 5-4)
Section 4.7.
Given A unit circle with radius = 1, center point at (0,0)
Presentation transcript:

Trigonometric Functions: The Unit Circle (Section 4-2)

The Unit Circle x2 + y2 = 1

Each value on the unit circle corresponds to a set of coordinates (x, y) = (cos, sin)

Determine the exact value of the six trig functions of the angle θ. Example 1 θ

Determine the exact value of the six trig functions of the angle θ. Example 2 θ

30° 45° 60° II I 120° 90° 2 Sin, csc + (students) 60° All + 1 135° 45° 150° 30° 180°,π 0°,2π IV 45° 1 210° 330° 225° 315° 60° 1 2 tan, cot + (take) 240° 300° cos, sec + (calculus) 270° III

A S C T ( , ) ( , ) ( , ) ( , ) ( , ) ( , ) ( , ) ( , ) ( , ) ( , ) (cos, sin) A (0, 1) S ( , ) 1 3 - ( , ) 1 3 2 2 2 2 ( , ) 2 2 ( , ) 2 2 - 2 2 2 2 ( , ) 3 1 ( , ) 3 1 - 2 2 2 2 (-1, 0) (1, 0) 2π π ( , ) 3 - 1 ( , ) 3 - 1 - 2 2 2 2 ( , ) 2 2 ( , ) 2 2 - - - 2 2 2 2 ( , ) 1 3 ( , ) 1 3 - - - C 2 2 2 2 (0, -1) T

Find the point (x, y) on the unit circle that corresponds to the real number t. Example 3

Find the point (x, y) on the unit circle that corresponds to the real number t. Example 4

Find the point (x, y) on the unit circle that corresponds to the real number t. Example 5

Evaluate the sine, cosine and tangent of the real number. Example 6

Evaluate the six trig functions of the real number. Example 7

Evaluate the trigonometric function using period as an aid Evaluate the trigonometric function using period as an aid. (Add/ Subtract 2π) Example 8

Evaluate the trigonometric function using period as an aid Evaluate the trigonometric function using period as an aid. (Add/ Subtract 2π) Example 9

Even and Odd Trig Functions cos (-t) = cos t sec (-t) = sec t Odd: sin (-t) = - sin t csc (-t) = - csc t tan (-t) = - tan t cot (-t) = - cot t

Use the value of the trig function to evaluate the indicated functions. Example 10 a) sin (-t) b) csc (-t)

Use the value of the trig function to evaluate the indicated functions. Example 11 a) cos (-t) b) sec (-t)

Use your calculator to evaluate the trigonometric function. Example 12

Use your calculator to evaluate the trigonometric function. Example 13

Use your calculator to evaluate the trigonometric function. Example 14

HW #13 pg 275 (37 – 48 all, 51 – 67 odd)