Notes 6-1: Radian Measure

Slides:

Advertisements

Similar presentations

Areas of Circles and Sectors

Advertisements

Angles and Their Measure Section 3.1. Objectives Convert between degrees, minutes, and seconds (DMS) and decimal forms for angles. Find the arc length.

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:

What is a RADIAN?!?!.

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.

Radian Measure. Many things can be measured using different units.

TOP 10 Missed Mid-Unit Quiz Questions. Use the given function values and trigonometric identities to find the indicated trig functions. Cot and Cos 1.Csc.

Warm-Up Find the following. 1.) sin 30 ◦ 2.) cos 270 ◦ 3.) cos 135 ◦

Can you draw a radius to each point of tangency? What do you notice about the radius in each picture?

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.

Arc Length & Area of a Sector (3.2) JMerrill, 2009.

Angles and Their Measure. 1. Draw each angle (Similar to p.105 #11-22)

Warm Up 1)Are the following functions periodic? 2) Write the equation of a cosine function given the following information: Amplitude = 5, Period = π,

Chapter 4: Circular Functions Review for Lessons 1 & 2 Mrs. Parziale.

And because we are dealing with the unit circle here, we can say that for this special case, Remember:

Radian Measure Advanced Geometry Circles Lesson 4.

6.1 Angles and Radian Measure Objective: Change from radian to degree measure and vice versa. Find the length of an arc given the measure of the central.

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.

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.

Trigonometry, 1.0: Students understand the notion of angle and how to measure it, in both degrees and radians. They can convert between degrees and radians.

Warm-up Using a white board, draw and label a unit circle with all degree and radian measures.

Section 7-2 Sectors of Circles SAS. Definition A sector of a circle is the region bounded by a central angle and the intercepted arc.

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.

Section 7.1 Angles and Their Measure Copyright © 2013 Pearson Education, Inc. All rights reserved.

Area of a circle.

Do Now Agenda Homework Handout (10 problems)  Do Do Now!

A little more practice You’ve got this! High five!

Drawing Angles in Standard Position

Section 4.1A Trigonometry (Degrees and Radians)

Radian and Degree Measure (part 2)

Arcs, Sectors & Segments

Radian Measure Gamma maths chapter33 radians to degrees, degrees to radians, angle and sector area.

Aim: How do we define radians and develop the formula

Convert each radian measure to degrees

11.6 Arc Lengths and Areas of Sectors

11.3 Areas of Circles and Sectors

Proportions in Circles

Do Now Find the value of each expression. Sin 60 ° Cos 30 ° Tan 270 °

2 Types of Answers Exact Rounded Use the Pi button on your calculator

Examples Radians & Degrees (part 2)

Convert degree measures of angles to radian measures, and vice versa.

6.1.5 – Sector Areas.

Warm-Up A circle has a diameter of 10 in. What is the arc length in radians of a sector with 135°? What is the arc length in radians of a sector with 95°?

Warm Up Write an equation for a cosine function with the following characteristics. Amplitude: 4 Period:  Phase shift: left 3 Vertical shift: down 4.

Arc length and area of a sector.

7.1 Radian and Degree measure

Objectives Convert angle measures between degrees and radians.

16.2 Arc Length and Radian Measure

Measuring Angles in Radians

Angles and Their Measures

Warm-Up: If , find tan θ..

9-2 and 11-3: Perimeter and Area of Circles and Sectors

47.75⁰ Convert to radians: 230⁰.

Unit 6 Day 2 Circle Relationships.

6.1 Angles and Radian Measure

13.2A General Angles Alg. II.

Chapter 2 Section 1.

Central Angles & Their Measures

Chapter 2 Section 1.

Measuring Angles in Radians

11.1: Circumference and Arc Length

Angles and Their Measure

Unit 4: Circles and Volume

Warm up: Solve for x 1.) 2.) 4.) 3.) 124◦ 70◦ x 18◦ x 260◦ x 20◦ 110◦

Adapted from Walch Education

Circle Review Bingo The solutions are linked. Click on the answer on the next slide and it will jump you to the slide that is the question to the solution.

EQ: How do you convert angle measures in

Angles and Their Measure

Presentation transcript:

Notes 6-1: Radian Measure Radian: The length of the corresponding arc on a unit circle. Arc: A “piece” of the circumference. Sector: A portion or “slice” of a circle. The arc length of the sector is the radian measure of θ.

C = 2πr (or C=πd) since r = 1 C = 2π(1) C = 2π Circumference: unit circle: radius = 1 1 full circle = 360° = 2π radians so…180° = π radians

Summary:

Finding the length of an arc on any circle. s = arc length r = radius θ = central angle in radians If the angle is given in degrees, then convert to radians before calculating the arc length.

p.348 5. Change 240° to radians.

9. Evaluate each expression without a calculator 9. Evaluate each expression without a calculator. (In other words, draw a unit circle and find the exact value.) *See next page for final solutions…

9. Now answer the given expressions (including part b and c)

Given the measurement of a central angle, find the length of its intercepted arc in a circle of radius 15 inches. Round to the nearest tenth. Reminder: s = rθ