Radian and Degree Measurements

Slides:



Advertisements
Similar presentations
Sec 6.1 Angle Measure Objectives:
Advertisements

Angles and Their Measure Section Angles Vertex Initial Side Terminal Side.
Radians In a circle of radius 1 unit, the angle  subtended at the centre of the circle by the arc of length 1 unit is called 1 radian, written as 1 rad.
3.2 Angle Measures in Degrees & Radians. Another way to measure angles is in radians. 360  = 2π rad.  180  = π rad. –To convert from degrees to radians:
Converting Degree Measure to Radian Measure Convert to radian measure: a)  or  π rad ≈ 3.67 Exact radian Approximate radian b) To.
13-3 Radian Measure Today’s Objective: I can measure an angle in radians.
And because we are dealing with the unit circle here, we can say that for this special case, Remember:
Warm-Up 3/26 Fahrenheit. Rigor: You will learn how to convert from degrees to radians and radians to degrees. Relevance: You will be able to solve real.
RADIAN THE UNIT CIRCLE. REMEMBER Find the circumference of a circle that has a radius of 1. C = 2πr C = 2π(1) C = 2π.
Arc Length Start with the formula for radian measure … … and multiply both sides by r to get … Arc length = radius times angle measure in radians.
Copyright © 2011 Pearson, Inc. 4.1 Angles and Their Measures.
Unit 1 – Degrees Decimals and Degrees, Minutes, Seconds (DMS) Conversions, and Unit Conversions -You will be able to convert from degrees decimals to degrees,
Everything you need to know , 5.5, 5.6 Review.
Unit 7: Angles and Angle Measures
Angles Arc Length Sector Area Section 4.1. Objectives I can find co-terminal angles I can convert between radian and degree measures I can calculate arc.
Review of Angles. Acute Angle – Angle less than 90 degrees Right Angle – Angle that is exactly 90 degrees.
Trigonometry Section 7.1 Find measures of angles and coterminal angle in degrees and radians Trigonometry means “triangle measurement”. There are two types.
Warm-up Using a white board, draw and label a unit circle with all degree and radian measures.
Coterminal Angles and Radian Measure
Topic 11-2 Radian Measure. Definition of a Radian Radian is the measure of the arc of a unit circle. Unit circle is a circle with a radius of 1.
Radians. Definition A radian is the angle that is subtended (cut out) at the center of the unit circle when the radius length and the arc length are equal.
Part 1.  We interpret an angle as a rotation of the ray R 1 onto R 2.  An angle measure of 1 degree is formed by rotating the initial side th of a complete.
Objectives: You will be able to convert between radians and degrees, find arc lengths. You will be able to define a radian. Agenda: 1.Do Now 2.Angles-Vocabulary.
Section 3-4 Radian Measures of Angles. Definition: Radian Measure of an Angle.
Drawing Angles in Standard Position
Grade Homework HW 13.2A Answers.
Arcs, Sectors & Segments
International Studies Charter School. Pre-Calculus Section 6-3
Radian Measure Gamma maths chapter33 radians to degrees, degrees to radians, angle and sector area.
Quadrants: Quarters on a coordinate plane
Trigonometry Review.
Section5.1 Angles and Their Measure
The Trigonometric Functions
Introduction to Trigonometry
9.3B Notes: Angle conversions
Angular Mechanics - Radians
Do Now Find the value of each expression. Sin 60 ° Cos 30 ° Tan 270 °
Aim: How do we convert radians to degrees and degrees to radians?
Examples Radians & Degrees (part 2)
Radians & Arc Lengths Section 5.2.
17-1 Angles of Rotation and Radian Measure
11–8A – Define Radian Measure
6.1 Radian and Degree Measure
Unit 8 The Unit Circle!.
Radian Measure of a Central Angle
Aim: How do we convert radians to degrees and degrees to radians?
Students, Take out your calendar and your homework. Take out your spiral notebook and Complete the DNA. Use your notes if necessary. Simplify.
Reference Angles & Unit Circle
Trig Functions and Acute Angles
Help I’m trapped in a nutshell
Things to Remember! , 5.5, 5.6 Review.
Trigonometric Equations with Multiple Angles
Angles and Their Measures
47.75⁰ Convert to radians: 230⁰.
Trigonometry Using Co-terminal and Reference Angles
6.1 Angles and Radian Measure
Unit 7B Review.
Chapter 2 Section 1.
Angles and Their Measure
Lesson The Unit Circle Objectives:
Central Angles & Their Measures
Chapter 2 Section 1.
Radian and Degree Measure
Section 4.1 Angles and Their Measure
( , ) ( , ) ( , ) ( , ) ( , ) ( , ) ( , ) ( , ) ( , ) ( , ) ( , )
Trig Graphs and reciprocal trig functions
EQ: Are there other ways to describe the location of a point in the plane other than by giving its x- and y- coordinates?
Conversions, Angle Measures, Reference, Coterminal, Exact Values
A circle with center at (0, 0) and radius 1 is called a unit circle.
Agenda Go over homework
Presentation transcript:

Radian and Degree Measurements Mr. Brenneman Ms. Walthall

1 -> 3 5 -> 11 8 -> 17 3 -> 11 5 -> 17 11 -> 35 Pattern: 1 -> 3 5 -> 11 8 -> 17 3 -> 11 5 -> 17 11 -> 35 4 -> 20 6 -> 40 8 -> 68 90 -> 180 -> π 135 ->    

Exploration Worksheet

Exploration Worksheet

Converting Angle Measure Degrees  Radians Multiply degrees by π rad 180° To apply conversions, use the relationship: π rad = 180°

Converting Angle Measure Radians  Degrees Multiply radians by 180° π rad To apply conversions, use the relationship: π rad = 180°

Co-Terminal Angles Find the relation between the following pairs of angles. Then write down a formula/rule that relates the two angles in each pair. π and 3π π/2 and 5π/2 7π/3 and π/3 π/4 and -7π/4