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

Slides:



Advertisements
Similar presentations
Circles Review Unit 9.
Advertisements

Objective: Convert between degrees and radians. Draw angles in standard form. Warm up Fill in the blanks. An angle is formed by two_____________ that have.
2.1 Angles and Their Measures
1 What you will learn  What radian measure is  How to change from radian measure to degree measure and vice versa  How to find the length of an arc.
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:
Radian Measure A central angle has a measure of 1 radian if it is subtended by an arc whose length is equal to the radius of the circle. Consider the circle.
Deriving the Formula for the Area of a Sector
What is a RADIAN?!?!.
7.2 Radian Measure.
Copyright © 2003 Pearson Education, Inc. Slide Radian Measure, Arc Length, and Area Another way to measure angles is using what is called radians.
Radian Measure Angles can be measured 3 ways: 1) Degrees (360 parts to a rotation) 1) Degrees (360 parts to a rotation) used for triangle applications.
Lesson 7-1 Angles, Arcs, and Sectors. Objective:
Converting between Degrees and Radians: Radian: the measure of an angle that, when drawn as a central angle of a circle, would intercept an arc whose.
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.
6.1.2 Angles. Converting to degrees Angles in radian measure do not always convert to angles in degrees without decimals, we must convert the decimal.
Section 5.2 – Central Angles and Arcs Objective To find the length of an arc, given the central angle Glossary Terms Arc – a part of a circle Central angle.
Copyright © 2011 Pearson Education, Inc. Radian Measure, Arc Length, and Area Section 1.2 Angles and the Trigonometric Functions.
Math III Accelerated Chapter 13 Trigonometric Ratios and Functions 1.
Radian Measure. Many things can be measured using different units.
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Section 7.1 Angles and Their Measure.
2.1 Continued! Warm-up Learning Objective: To understand what a radian is and how they relate to degrees to be able to convert radians to degrees and degrees.
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 ◦
Trigonometry #3 Radian Measures. Converting Degrees to Radians Angle measure In degrees.
Can you draw a radius to each point of tangency? What do you notice about the radius in each picture?
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Section 6.1 Angles and Their Measure.
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.
Warm Up 1)Are the following functions periodic? 2) Write the equation of a cosine function given the following information: Amplitude = 5, Period = π,
Arc Length and Sector Area. How do we get the fraction in these formulas? How many degrees are in a circle? Fraction = (central angle/360)
RADIANS Radians, like degrees, are a way of measuring angles.
And because we are dealing with the unit circle here, we can say that for this special case, Remember:
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.
6-1 Angle Measures The Beginning of Trigonometry.
7.2 – Sectors of Circles Essential Question: How do you find the radius of a sector given its’ area and arc length?
Section 2.1 Angles and Their Measure. Sub-Units of the Degree: “Minutes” and “Seconds” (DMS Notation)
Unit 1 – Degrees Decimals and Degrees, Minutes, Seconds (DMS) Conversions, and Unit Conversions -You will be able to convert from degrees decimals to degrees,
Measuring Angles – Radian Measure Given circle of radius r, a radian is the measure of a central angle subtended by an arc length s equal to r. The radian.
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.
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Section 7.1 Angles and Their Measure.
Radian Measure Advanced Geometry Circles Lesson 4.
Radian Measure That was easy
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.
1° = 60 ′ 1 ′ = 60 ″ Convert 50°6 ′ 21 ″ 50° + 6 × (1/60)° + 21 × (1/60) × (1/60)° = ° Convert to degrees 21° +.256(60 ′ ) 21° ′
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.
Unit Circle. Special Triangles Short Long Hypotenuse s s 2s Hypotenuse 45.
Warm Up Identify the parts of the circle 10 minutes End.
Section 7.1 Angles and Their Measure Copyright © 2013 Pearson Education, Inc. All rights reserved.
A little more practice You’ve got this! High five!
Drawing Angles in Standard Position
Aim: How do we define radians and develop the formula
Angles and Their Measure
Angles and Their Measure
Notes 6-1: Radian Measure
Angles and Their Measure
Angles and Their Measure
Examples Radians & Degrees (part 2)
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.
Angles and Their Measure
16.2 Arc Length and Radian Measure
Angles and Their Measure
Angles and Their Measure
Angles and Their Measures
6.1 Angles and Radian Measure
Arc Length, Sector Area, and Inscribed Angles
Angles and Their Measure
Angles and Their Measure
Angles and Their Measure
Presentation transcript:

Angles and Their Measure

1. Draw each angle (Similar to p.105 #11-22)

2. Draw each angle (Similar to p.105 #11-22)

3. Draw each angle (Similar to p.105 #11-22)

4. Convert each angle to a decimal in degrees. Round your answer to two decimal places (Similar to p.105 #23-28)

5. Convert each angle to D o M′S′′ form. Round your answer to the nearest second (Similar to p.106 #29-34)

6. Convert each angle in degrees to radians. Express your answer as a multiple of π (Similar to p.106 #35-46)

7. Convert each angle in degrees to radians. Express your answer as a multiple of π (Similar to p.106 #35-46)

8. Convert each angle in radians to degrees. (Similar to p.106 #47-58)

9. Convert each angle in degrees to radians. Express your answer in decimal form, rounded to two decimal places (Similar to p.106 #59-64)

10. Convert each angle in radians to degrees. Express your answer in decimal form, rounded to two decimal places (Similar to p.106 #65-70)

11. s denotes the length of the arc of a circle of radius r subtended by the central angle θ. Find the missing quantity. Round answers to three decimal places. Formula: s=rθ (Similar to p.106 #71-78)

12. s denotes the length of the arc of a circle of radius r subtended by the central angle θ. Find the missing quantity. Round answers to three decimal places. Formula: s=rθ (Similar to p.106 #71-78)

13. A denotes the area of the sector of a circle of radius r formed by the central angle θ. Find the missing quantity. Round answers to three decimal places. (Similar to p.106 #79-86)

14. Find the length s and area A. Round answers to three decimal places (Similar to p.106 #87-90)