The Unit Circle Part I MSpencer. The Unit Circle r = 1 It is called a unit circle because the radius is one unit.

Slides:



Advertisements
Similar presentations
Angles of Rotation and Radian Measure In the last section, we looked at angles that were acute. In this section, we will look at angles of rotation whose.
Advertisements

Warm Up Find the measure of the supplement for each given angle °2. 120° °4. 95° 30°60° 45° 85°
5.1 Angles and Degree Measures. Definitions An angle is formed by rotating one of two rays that share a fixed endpoint know as the vertex. The initial.
Coterminal Angles. What are coterminal angles? Two angles in standard position that have the same terminal side are called coterminal. Initial side Terminal.
What Is A Radian? 1 radian = the arc length of the radius of the circle.
Angles and Arcs in the Unit Circle Radian and Degree Measure In this section, we will study the following topics: Terminology used to describe.
MTH 112 Elementary Functions Chapter 5 The Trigonometric Functions Section 4 – Radians, Arc Length, and Angular Speed.
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.
Definition of Trigonometric Functions With trigonometric ratios of acute angles in triangles, we are limited to angles between 0 and 90 degrees. We now.
Finding Exact Values of Trig Ratios. Special Right Triangles
What is a RADIAN?!?!.
7.2 Radian Measure.
13.2 Angles and Angle Measure
Day 2 Students will be able to convert between radians and degrees. Revolutions, Degrees, and Radians.
13-3: Radian Measure Radian Measure There are 360º in a circle The circumference of a circle = 2r. So if the radius of a circle were 1, then there a.
13.3 Radian Measure A central angle of a circle is an angle with a vertex at the center of the circle. An intercepted arc is the portion of the circle.
Chapter 13 Section 3 Radian Measure.
Radian Measure. Many things can be measured using different units.
Try describing the angle of the shaded areas without using degrees.
Introduction to Unit Circle Trigonometry 1. The Unit Circle on the Coordinate Plane (1,0) (0,1) (-1,0) (0, -1) Quadrant I X – Pos Y - Pos X Y Radius =
30º 60º 1 45º 1 30º 60º 1 Do Now: Find the lengths of the legs of each triangle.
Aim: How do we define radians and develop the formula Do Now: 1. The radius of a circle is 1. Find, in terms of the circumference. 2. What units do we.
13-3 Radian Measure Today’s Objective: I can measure an angle in radians.
Terms to know going forward Angle: 2 rays an initial side and a terminal side. Initial side Terminal side Positive angle goes counter clockwise. Negative.
RADIANS Radians, like degrees, are a way of measuring angles.
The Unit Circle Part II (With Trig!!) MSpencer. Multiples of 90°, 0°, 0 360°, 2  180°,  90°, 270°,
Section 6.1 Notes Special Angles of the Unit Circle in degrees and radians.
Objectives Change from radian to degree measure, and vice versa Find angles that are co-terminal with a given angle Find the reference angle for a given.
C2:Radian Measure Learning Objective: to understand that angles can be measured in radians.
And because we are dealing with the unit circle here, we can say that for this special case, Remember:
13.2 Angles of Rotation and Radian Measure
MEASURES of ANGLES: RADIANS FALL, 2015 DR. SHILDNECK.
Radian Measure of a Circle another way to measure angles!
Intro to radians and unit circle F-TF.1 F-TF.2 ANGLES AND ANGLE MEASURE.
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.
Trigonometry Exact Value Memory Quiz A Trigonometry Exact Value Memory Quiz A.
4.1 Radian and Degree Measure (part 2) V. Evaluating degrees° minutes’ seconds” (D°M’S”) A) The distance between two degrees (ex: 15°& 16°) can be 1) divided.
LESSON 6-1: ANGLES & THE UNIT CIRCLE BASIC GRAPHING OBJECTIVE: CONVERT BETWEEN DEGREE AND RADIAN MEASURE, PLACE ANGLES IN STANDARD POSITION & IDENTIFY.
Radian Angle Measures 1 radian = the angle needed for 1 radius of arc length on the circle still measures the amount of rotation from the initial side.
Unit 7: Angles and Angle Measures
Unit Circle Review Degrees and Radians.
Perimeter and Area with Circles. Circumference of a Circle Circumference is the perimeter of the circle Formula: or (for exact answers, leave π in your.
Holt McDougal Geometry 12-3-EXT Measuring Angles in Radians 12-3-EXT Measuring Angles in Radians Holt Geometry Lesson Presentation Lesson Presentation.
14.1 The Unit Circle Part 2. When measuring in radians, we are finding a distance ____ the circle. This is called. What is the distance around a circle?
Coterminal Angles and Radian Measure
More Trig - Radian Measure and Arc Length Warm-up Learning Objective: To convert from degree measure to radian measure and vice versa and to find arc length.
Unit Circle. Special Triangles Short Long Hypotenuse s s 2s Hypotenuse 45.
Reclaiming a Language James Nixon Topic: π and degree conversion 11 th Grade March 9, 2010.
Unit 3 Trigonometry Review Radian Measure Special Angles Unit Circle 1.
Angles and the Unit circle
6.1 Radian and Degree Measure
Warm Up 4) 30° 5)
9.3B Notes: Angle conversions
Two angles in standard position that share the same terminal side.
Radian Measure of a Central Angle
Measuring Angles in Radians
Trig Functions and Acute Angles
Coterminal Angles.
pencil, highlighter, calculator, notebook
pencil, red pen, highlighter, calculator, notebook
U8D9 pencil, highlighter, red pen, calculator, notebook Have out:
U8D4 Have out: pencil, red pen, highlighter, notebook, calculator, assignment Bellwork: 1. Convert the following angles from degrees to radians. a) 30
pencil, red pen, highlighter, calculator, notebook
Warm-up: Determine the circumference of the following circles in terms of π. HW: p (5 – 10 , , 25, 27, 33 – 36 , 43 – 61 odd, 71, 73)
pencil, red pen, highlighter, packet, notebook, calculator
( , ) ( , ) ( , ) ( , ) ( , ) ( , ) ( , ) ( , ) ( , ) ( , ) ( , )
EQ: Are there other ways to describe the location of a point in the plane other than by giving its x- and y- coordinates?
Unit 4: Circles and Volume
Presentation transcript:

The Unit Circle Part I MSpencer

The Unit Circle r = 1 It is called a unit circle because the radius is one unit.

All the Way Around Another way of measuring angles is with radians. Since a revolution is the circumference of a circle and r = 1, C = 2  r = 2  (1) = 2  r = 1 One way to measure angles is with degrees. One revolution around the unit circle constitutes 360°. 2  radians is equivalent to 360°

One Revolution r = 1 0°, 0 360°, 2 

Multiples of 90°, 0°, 0 360°, 2  180°,  90°, 270°,

The Quadrants 0°, 0 360°, 2  180°,  90°, 270°, Q I 0° <  < 90° 0 <  < QII 90° <  < 180° <  <  QIII 180° <  < 270°  <  < QIV 270° <  < 360° <  < 2 

Multiples of 45°, 135°, 315°, 45°,225°,

Multiples of 60°, 120°, 300°, 60°,240°,

Multiples of 30°, 150°, 330°, 30°,210°,

The Whole Unit Circle Together (Grouped) 150°, 330°, 30°,210°, 0°, 0 360°, 2  180°,  90°, 270°, 135°, 315°, 45°,225°,120°, 300°, 60°,240°,

The Whole Unit Circle Together (In Ascending Order) 150°, 330°, 30°,210°, 0°, 0 360°, 2  180°,  90°, 270°, 135°, 315°, 45°,225°,120°, 300°, 60°,240°,