January 19 th in your BOOK, 4.2 copyright2009merrydavidson.

Slides:

Advertisements

Similar presentations

Math 4 S. Parker Spring 2013 Trig Foundations. The Trig You Should Already Know Three Functions: Sine Cosine Tangent.

Advertisements

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

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.

Section 5.3 Trigonometric Functions on the Unit Circle

Section Review right triangle trigonometry from Geometry and expand it to all the trigonometric functions Begin learning some of the Trigonometric.

Copyright © 2009 Pearson Addison-Wesley Trigonometric Functions.

Trigonometric Ratios Triangles in Quadrant I. a Trig Ratio is … … a ratio of the lengths of two sides of a right Δ.

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.

Right Triangle Trigonometry Digital Lesson. Copyright © by Houghton Mifflin Company, Inc. All rights reserved. 2 The six trigonometric functions of a.

MAT170 SPR 2009 Material for 3rd Quiz. Sum and Difference Identities: ( sin ) sin (a + b) = sin(a)cos(b) + cos(a)sin(b) sin (a - b) = sin(a)cos(b) - cos(a)sin(b)

5.2-The Unit Circle & Trigonometry. 1 The Unit Circle 45 o 225 o 135 o 315 o 30 o 150 o 110 o 330 o π6π6 11π 6 5π65π6 7π67π6 7π47π4 π4π4 5π45π4 3π43π4.

Right Triangle Trigonometry Trigonometry is based upon ratios of the sides of right triangles. The six trigonometric functions of a right triangle, with.

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,

Chapter 3 Trigonometric Functions of Angles Section 3.2 Trigonometry of Right Triangles.

Section 5.3 Trigonometric Functions on the Unit Circle

 Angles and Degree Measure › An angle is formed by two rays with a common endpoint › That endpoint is called the vertex › Angles can be labeled by the.

Trigonometric Functions Of Real Numbers

Aim: What are the reciprocal functions and cofunction? Do Now: In AB = 17 and BC = 15. 1) Find a) AC b) c) d) 2) Find the reciprocal of a)b) c) A B C.

Trigonometry for Any Angle

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

12-2 Trigonometric Functions of Acute Angles

Right Triangle Trigonometry

Chapter 4 Trigonometric Functions Right Triangle Trigonometry Objectives:  Evaluate trigonometric functions of acute angles.  Use fundamental.

Bell Work Find all coterminal angles with 125° Find a positive and a negative coterminal angle with 315°. Give the reference angle for 212°.

January 20 th BOOK 4.2 copyright2009merrydavidson.

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)

Right Triangle Trigonometry Obejctives: To be able to use right triangle trignometry.

13.7 (part 2) answers 34) y = cos (x – 1.5) 35) y = cos (x + 3/(2π)) 36) y = sin x –3π 37) 38) y = sin (x – 2) –4 39) y = cos (x +3) + π 40) y = sin (x.

Do Now: Graph the equation: X 2 + y 2 = 1 Draw and label the special right triangles What happens when the hypotenuse of each triangle equals 1?

4.2 Trigonometric Functions (part 2) III. Trigonometric Functions. A) Basic trig functions: sine, cosine, tangent. B) Trig functions on the unit circle:

Graphs of the Trig Functions Objective To use the graphs of the trigonometric functions.

October 29, 2012 The Unit Circle is our Friend! Warm-up: Without looking at your Unit Circle! Determine: 1) The quadrant the angle is in; 2) The reference.

14.2 The Circular Functions

1 What you will learn  How to find the value of trigonometric ratios for acute angles of right triangles  More vocabulary than you can possibly stand!

Section 5.3 Evaluating Trigonometric Functions

Chapter 5 – Trigonometric Functions: Unit Circle Approach Trigonometric Function of Real Numbers.

5.3 The Unit Circle. A circle with center at (0, 0) and radius 1 is called a unit circle. The equation of this circle would be So points on this circle.

5.2 – Day 1 Trigonometric Functions Of Real Numbers.

Reciprocal functions secant, cosecant, cotangent Secant is the reciprocal of cosine. Reciprocal means to flip the ratio. Cosecant is the reciprocal of.

Warm up Solve for the missing side length. Essential Question: How to right triangles relate to the unit circle? How can I use special triangles to find.

December 14th BOOK 4.2 copyright2009merrydavidson

Objectives : 1. To use identities to solve trigonometric equations Vocabulary : sine, cosine, tangent, cosecant, secant, cotangent, cofunction, trig identities.

4.2 Trig Functions of Acute Angles. Trig Functions Adjacent Opposite Hypotenuse A B C Sine (θ) = sin = Cosine (θ ) = cos = Tangent (θ) = tan = Cosecant.

Section 13.1.a Trigonometry. The word trigonometry is derived from the Greek Words- trigon meaning triangle and Metra meaning measurement A B C a b c.

Lesson 46 Finding trigonometric functions and their reciprocals.

Warm up. Right Triangle Trigonometry Objective To learn the trigonometric functions and how they apply to a right triangle.

Bellringer 3-28 What is the area of a circular sector with radius = 9 cm and a central angle of θ = 45°?

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

4.4 Day 1 Trigonometric Functions of Any Angle –Use the definitions of trigonometric functions of any angle –Use the signs of the trigonometric functions.

Trig Functions – Part Pythagorean Theorem & Basic Trig Functions Reciprocal Identities & Special Values Practice Problems.

Precalculus 4.3 Right Triangle Trigonometry 1 Bellwork Rationalize the denominators ·

13.1 Right Triangle Trigonometry ©2002 by R. Villar All Rights Reserved.

13.1 Right Triangle Trigonometry. Definition  A right triangle with acute angle θ, has three sides referenced by angle θ. These sides are opposite θ,

Bell Work 1.Find all coterminal angles with 125° 1.Find a positive and a negative coterminal angle with 315°. 1.Give the reference angle for 212°. 1.Find.

Right Triangle Trigonometry

Lesson Objective: Evaluate trig functions.

Section 4.2 The Unit Circle.

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

Warm-Up: February 3/4, 2016 Consider θ =60˚ Convert θ into radians

Warm-Up: Give the exact values of the following

Right Triangle Ratios Chapter 6.

Trigonometric Functions: The Unit Circle 4.2

WArmup Rewrite 240° in radians..

θ hypotenuse adjacent opposite θ hypotenuse opposite adjacent

Academy Algebra II THE UNIT CIRCLE.

Presentation transcript:

January 19 th in your BOOK, 4.2 copyright2009merrydavidson

Special Right Triangles S O H C A H T O A

y x r Reciprocal functions Parent functions

Reciprocal Identities Memorize these 11 identities for a quiz SOON!!!

Look at your unit circle now… cosine sine Check out the Pythagorean Identities

Evaluating Trig Functions: 1: Find the six trig. values for 300 . sin 300 o = csc 300 o = cos 300 o = sec 300 o = tan 300 o =cot 300 o = Use your Plate, find the angle, evaluate. Rationalize the denominator as needed.

Evaluating Trig Functions: 2: Find the six trig. values for -5  /4. sin = csc = cos = sec = tan =cot = Use your Plate, find the angle, evaluate. Rationalize the denominator as needed.

Find the sine of the angles listed. 30 o =390 o =-330 o = What is the NAME of the type of these 3 angles? What conclusion can you make? Co-terminal angles have the same trig values. It takes 360 o to get to the same trig value, thus the PERIOD for the sine and cosecant function is 360 o co-terminal angles

Find the cosine of the angles listed. 60 o =420 o =-300 o = It takes 360 o to get to the same place, thus the PERIOD for the cosine and secant function is 360 o or.

Find the tangent of the angles listed. 45 o =225 o =-135 o = It takes 180 o to get the same trig value, thus the PERIOD for the tangent and cotangent function is 180 o.

Summary of Period sin/csc/cos/sec have a period of 360 o. tan/cot have a period of BE CAREFUL TO NOT USE CAPITAL LETTERS. WE WILL LEARN THAT LATER

y = sin x Is this an even or odd function? y = csc x is also odd.

y = cos x Is this an even or odd function? y = sec x is also even

y = tan x Is this an even or odd function? y = cot x is also odd

Now look at the even/odd Identities What does this mean????

Trig Identities f(x) = cos xf(x) = sin x EVEN ODD

Problems 1)If sin (t) = ¼, find sin (-t). 2)If sin (t) is 3/8, find csc (-t). 3) If cos (t) = -3/4, find cos(-t). -1/4 If sin (t) is 3/8, then csc (t) = 8/3. We want to find csc (-t) which is the opposite of csc (t) = -8/3. cos(t) = cos(-t) so = -3/4

Trig Identities f(x) = tan x ODD If tan (t) = 2/3 find tan (-t). -2/3

HW: WS 6-4