Put all unit circles away and prepare to take the “Unit Circle Quiz.”

Slides:



Advertisements
Similar presentations
1.4 - Trigonometric Functions of Any Angle
Advertisements

Pg. 472 Homework Pg. 324#70 – 76 all #1ɣ = 68°, b = 3.88, c = 6.61 #2α = 35.97°, ɣ = 34.03°, c = 4.76 #3 = °, b = 27.55, c = #4No triangle.
Angles and Radian Measure Section 4.1. Objectives Estimate the radian measure of an angle shown in a picture. Find a point on the unit circle given one.
Definition of Trigonometric Functions With trigonometric ratios of acute angles in triangles, we are limited to angles between 0 and 90 degrees. We now.
4.1: Radian and Degree Measure Objectives: To use radian measure of an angle To convert angle measures back and forth between radians and degrees To find.
Chapter Radian and degree measurement. Objectives O Describe Angles O Use radian measure O Use degree measure and convert between and radian measure.
Ch 4 Trigonometric Functions
Trigonometric Functions
Arc Lengths, Sectors, and Rotational Speeds Dr. Shildneck Fall, 2014.
Chapter 4 Trigonometric Functions Trig Functions of Any Angle Objectives:  Evaluate trigonometric functions of any angle.  Use reference angles.
4.4 – Trigonometric Functions of any angle. What can we infer?? *We remember that from circles anyway right??? So for any angle….
Radian and Degree Measure
4.1 Day 2 Objectives: Find coterminal angles Find the length of a circular arc Use linear & angular speed to describe motion on a circular path Pg. 459.
4.3 Right Triangle Trig. Remembering SOHCAHTOA Let  be an acute angle of a right triangle. Then…
Right Triangle Trigonometry Identify the parts of a right triangle hypotenuse opposite adjacent an acute angle in the triangle ''theta'' θ.
Splash Screen. Lesson Menu Five-Minute Check (over Lesson 4-1) Then/Now New Vocabulary Example 1:Convert Between DMS and Decimal Degree Form Key Concept:Radian.
Copyright © 2014, 2010, 2007 Pearson Education, Inc.
Copyright © 2014 Pearson Education, Inc.
Circular Functions & Trig Identities 2: Solving Trig Equations
Copyright © 2014, 2010, 2007 Pearson Education, Inc.
Copyright © 2014, 2010, 2007 Pearson Education, Inc.
Section5.1 Angles and Their Measure
Radian and Degree Measure
Recall Radian measure:
Warm Up Use trigonometric identities to simplify: csc ∙tan
Splash Screen.
Chapter 4: Lesson 4.1 Radian & Degrees
Convert degree measures of angles to radian measures, and vice versa.
1) Find the measure of the largest angle.
Radian and Degree Measures
Evaluate each expression. Hint: Use the unit circle.
Reference Angles & Unit Circle
Trig Functions and Acute Angles
Help I’m trapped in a nutshell
Complete each identity.
1) On a blank unit circle fill in the degree measures.
Back to Trig Quick Review: Convert 200 degrees to radians
Find the missing parts of each triangle.
1) State the LAW OF SINES. 2) Find a. Students,
Simplify the expression using a sum/difference formula.
Convert the following angle to radians or vice versa.
TRIGONOMETRIC FUNCTIONS OF ANY ANGLE
Use the same sheet of paper as yesterday.
Without a calculator, find the indicated value.
Copyright © 2014, 2010, 2007 Pearson Education, Inc.
Use the same sheet of paper as yesterday.
Write the complement and supplement of each angle.
Complete each trigonometric identity. Factor each expression.
Find all the solutions without using a calculator.
Degrees and radians.
Precalculus Essentials
Warm-up: Find the tan 5
4.4 Trig Functions of any Angle
Students, Take out your calendar and your homework. Take out your spiral notebook and Complete the DNA. Use your notes if necessary. 3) Write the degree.
LESSON 4–2 Degrees and Radians.
Find all the solutions without using a calculator.
Find the period and amplitude. Describe the shift.
Circular Trigonometric Functions.
Section 4.1 Angles and Their Measure
Take out a sheet of paper for the short quiz.
1) Write the vector in component form.
13-2 Angles and Angle Measure
Find all the solutions without using a calculator.
Complete each identity
Find the exact value of each expression.
Evaluate each expression. Hint: Use the unit circle.
Complete each table. Students,
Find the amplitude and period for each function.
Complete each identity
Linear and Angular Speed
Presentation transcript:

Put all unit circles away and prepare to take the “Unit Circle Quiz.” Students, Take out your calendar and your homework. Take out your spiral notebook and Complete the DNA. Use your notes if necessary. Put all unit circles away and prepare to take the “Unit Circle Quiz.”

Complete each identity. Students, Take out your calendar and your homework. Take out your spiral notebook and Complete the DNA. Use your notes if necessary. Complete each identity.

Not possible, we don’t know if “theta” is in quad I or quad II. Recall sohcahtoa and draw a triangle. Not possible, we don’t know if “theta” is in quad I or quad II.

Trigonometric Values of Common Angles Unit Circle x y (0, 1) 90° 120° 60° 135° 45° 30° 150° (–1, 0) 180° (1, 0) 0° 360° 210° 330° 315° 225° 240° 300° (0, –1) 270° Trigonometric Values of Common Angles

y x

Definitions of Trig Functions of Any Angle

Reference Angle Let θ be an angle in standard position. Its reference angle is the acute angle θ´ formed by the terminal side of θ and the horizontal axis.

4) A tree makes a shadow 35 feet long 4) A tree makes a shadow 35 feet long. The angle of elevation to the sun is 13. How tall is the tree? Solve each triangle. 6) 5)

Linear and Angular Speed 2) The circular blade on a saw rotates at 2400 revolutions per minute. Find the angular speed in radians per second. The blade has a radius of 4 inches. Find the linear speed of a blade tip in inches per second.