 Find the value of the other five trigonometric functions.

Slides:



Advertisements
Similar presentations
Splash Screen. Lesson Menu Five-Minute Check (over Lesson 8–3) NGSSS Then/Now New Vocabulary Key Concept: Trigonometric Ratios Example 1: Find Sine, Cosine,
Advertisements

The Inverse Trigonometric Functions Section 4.2. Objectives Find the exact value of expressions involving the inverse sine, cosine, and tangent functions.
Evaluating Sine & Cosine and and Tangent (Section 7.4)
Trig Functions of Special Angles
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.
Copyright © Cengage Learning. All rights reserved. Trigonometric Functions: Right Triangle Approach.
5.5 Solving Trigonometric Equations Example 1 A) Is a solution to ? B) Is a solution to cos x = sin 2x ?
Section 7-4 Evaluating and Graphing Sine and Cosine Objectives: To use the reference angles, calculators and tables and special angles to find the values.
Essential Question: What are the restricted domains for the sin, cos, and tan functions?
 Given that and find the value of the cos θ.  Memorize it!  Quiz 1 st week of 2 nd semester ◦ 8 minute time limit ◦ All or nothing ◦ 20 points 
Copyright © 2009 Pearson Education, Inc. CHAPTER 7: Trigonometric Identities, Inverse Functions, and Equations 7.1Identities: Pythagorean and Sum and.
Chapter 6: Trigonometry 6.5: Basic Trigonometric Identities
10.3 Verify Trigonometric Identities
Trigonometry (RIGHT TRIANGLES).
8.3 Solving Right Triangles
5-5 Solving Right Triangles. Find Sin Ѳ = 0 Find Cos Ѳ =.7.
EXAMPLE 1 Finding Trigonometric Ratios For PQR, write the sine, cosine, and tangent ratios for P. SOLUTION For P, the length of the opposite side is 5.
Sine, Cosine and Tangent Ratios Objective Students will be able to use sine, cosine, and tangent ratios to determine side lengths in triangles.
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.
Friday, February 5 Essential Questions
Sum and Difference Formulas New Identities. Cosine Formulas.
Section 6.4 Inverse Trigonometric Functions & Right Triangles
Finding an angle. (Figuring out which ratio to use and getting to use the 2 nd button and one of the trig buttons. These are the inverse functions.) 5.4.
13.2 – Define General Angles and Use Radian Measure.
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.
Sec 6.2 Trigonometry of Right Triangles Objectives: To define and use the six trigonometric functions as ratios of sides of right triangles. To review.
Section 8.5 Tangent Ratio. What is Trigonometry ? The study of triangles and their measurements.
Slide Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley.
Warm- Up 1. Find the sine, cosine and tangent of  A. 2. Find x. 12 x 51° A.
SECTION 8.4 TRIGONOMETRY. The word trigonometry comes from two greek terms, trigon, meaning triangle, and metron, meaning measure. a trigonometric ratio.
Chapter 4: Circular Functions Lesson 4: Trigonometric Identities Mrs. Parziale.
Trig Functions of Angles Right Triangle Ratios (5.2)(1)
4.4 Trigonometric Functions of Any Angle
Evaluating Inverse Trigonometric Functions
Computing the Values of Trigonometric Functions of Acute Angles Section 3.3.
Properties of the Trigonometric Functions
Sin, Cos, Tan with a calculator  If you are finding the sin, cos, tan of an angle that is not a special case (30, 60, 45) you can use your calculator.
Notes Over 6.3 Evaluating Trigonometric Functions Given a Point Use the given point on the terminal side of an angle θ in standard position. Then evaluate.
Section 6.2 Trigonometric Functions: Unit Circle Approach.
Section 7.4 Inverses of the Trigonometric Functions Copyright ©2013, 2009, 2006, 2001 Pearson Education, Inc.
Right Triangles Consider the following right triangle.
Section 1 – Trigonometry and the Graphing Calculator After this section, you should be able to show that you can: Know the SIX trig. functions Change degree-minutes.
4.7 – Square Roots and The Pythagorean Theorem Day 2.
Right Triangle Trig: Finding a Missing Angle. Finding an angle. (Figuring out which ratio to use and getting to use the 2 nd button and one of the trig.
EXAMPLE 2 Find cosine ratios Find cos U and cos W. Write each answer as a fraction and as a decimal. cos U = adj. to U hyp = UV UW = cos W.
Check it out Does the sin(75) =sin(45)+sin(30) ?.
Warm-Up 2/12 Evaluate – this is unit circle stuff, draw your triangle.
MATH 110 UNIT 1 – TRIGONOMETRY Part A. Activity 7 – Find Missing Sides To find an unknown side on a triangle, set up our trigonometric ratios and use.
Warm – up Find the sine, cosine and tangent of angle c.
8.4 Trigonometry- Part I Then: You used the Pythagorean Theorem to find missing lengths in right triangles. Now: 1. Find trigonometric ratios using right.
Splash Screen. Then/Now You used the Pythagorean Theorem to find missing lengths in right triangles. Find trigonometric ratios using right triangles.
Pythagorean Identities Unit 5F Day 2. Do Now Simplify the trigonometric expression: cot θ sin θ.
Lesson 8-6 The Sine and Cosine Ratios (page 312) The sine ratio and cosine ratio relate the legs to the hypotenuse. How can trigonometric ratios be used.
Trigonometry Section 7.4 Find the sine and cosine of special angles. Consider the angles 20 o and 160 o Note: sin 20 o = sin160 o and cos 20 o = -cos 160.
Trig Functions – Part Pythagorean Theorem & Basic Trig Functions Reciprocal Identities & Special Values Practice Problems.
Trigonometric Ratios How do you use trig ratios? M2 Unit 2: Day 4.
Trigonometry Section 7.6 Apply inverse trigonometry functions
Section 1.3 Reference Angles.
Section 18.3: Special Right Triangles
7.7 Solve Right Triangles Obj: Students will be able to use trig ratios and their inverses to solve right triangles.
Section 12-1a Trigonometric Functions in Right Triangles
Warm – Up: 2/4 Convert from radians to degrees.
Inverses of the Trigonometric Functions
Inverse Trigonometric Functions (Section 4-7)
Trigonometric Functions:
Review these 1.) cos-1 √3/ ) sin-1-√2/2 3.) tan -1 -√ ) cos-1 -1/2
Right Triangle Trigonometry
Geometry Section 7.7.
Trigonometric Functions:
Presentation transcript:

 Find the value of the other five trigonometric functions.

Section 4.7

 Ensure that your calculator is set to radians [MODE]  ensure “Radian” is highlighted  [2nd] [SIN]  sin -1  [2nd] [COS]  cos -1  [2nd] [TAN]  tan -1

 Use a calculator to find the value (in radians) to four decimal places of:

 Read Section 4.7  Page 522 #1-29 Odd  Page 522 #31-69 Odd

 20 questions, 5 points each  100 points possible 5 th Period6 th Period Minimum3935 Mean Median Maximum10096

 In Exercises 1-18, find the exact value of each expression.  In Exercises 19-30, use a calculator to find the value of each expression rounded to four decimal places.

 Find the inverse of  Look back at your notes from 1.8 if you don’t remember how to do this.

 Find the exact value, if possible, of:

 Read Section 4.7  Page 522 #1-?? Odd  Page 522 #??-69 Odd

 Simplify each of the following

 Find the exact value of

1. Look at your inner function to determine what quadrant the angle is in 2. Draw a right triangle that fits your inner function 3. Use the Pythagorean Theorem (or Pythagorean Triples) to find the other side length 4. Use the triangle to find the outer function value

 Find the exact value of

 Write an algebraic expression for

 Read Section 4.7  Page 522 #1-29 Odd  Page 522 #31-69 Odd