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IB Revision: Radians, Arcs, Sectors Relationship between radians and degrees: 0/360 ° 90 ° 180 ° 270 ° 0/2π ½ π π 3/2 π e.g. 1)45 ° = 2)60° = 3)300° = 4)20°= 5)182°=
IB Revision: Radians, Arcs, Sectors NameWhat we find FormulaUnit 10 cm θ
IB Revision: Radians, Arcs, Sectors NameWhat we find FormulaUnit ArcLengthcm 10 cm θ
IB Revision: Radians, Arcs, Sectors NameWhat we find FormulaUnit ArcLengthcm 5 m θ
IB Revision: Radians, Arcs, Sectors NameWhat we find FormulaUnit ArcLengthcm SectorAream2m2 5 m θ
IB Revision: Radians, Arcs, Sectors NameWhat we find FormulaUnit ArcLengthcm SectorAream2m2 θ 1 km
IB Revision: Radians, Arcs, Sectors NameWhat we find FormulaUnit ArcLengthcm SectorAream2m2 SectorAreakm 2 θ 1 km
IB Revision: Radians, Arcs, Sectors NameWhat we find FormulaUnit ArcLengthcm SectorAream2m2 SectorAreakm 2 3 ft θ
IB Revision: Radians, Arcs, Sectors NameWhat we find FormulaUnit ArcLengthcm SectorAream2m2 SectorAreakm 2 SectorLengthft 2 3 ft θ
IB Revision: Radians, Arcs, Sectors NameWhat we find FormulaUnit ArcLengthcm SectorAream2m2 SectorAreakm 2 SectorLengthft 2 5 mm θ
IB Revision: Radians, Arcs, Sectors NameWhat we find FormulaUnit ArcLengthcm SectorAream2m2 SectorAreakm 2 SectorLengthft SegmentAreamm 2 5 mm θ
IB Revision: Radians, Arcs, Sectors Find the length of the minor arc Find the area of the sector
IB Revision: Radians, Arcs, Sectors
RADIANS Definition An arc of length r subtends an angle of one radian at the centre of a circle of radius r r r r Ø=1radian.
1.Start by substituting another variable (like y) for 2x and solve like we have before, BUT you must include all answers in the specified domain 2.Then.
10 mm is the same as... 1 cm. 20 mm is the same as... 2 cm.
Chapter 4-2: Lengths of Arcs and Areas of Sectors.
+90° -90° -180° -270° a( ) lg( ) 0’dB ()() lg( ) 0°
When solving trig equations there are a few things to keep in mind: 1.Before you solve any trig equation, check the domain of the problem. (Is it asking.
9.2 Define General Angles and Use Radian Measure What are angles in standard position? What is radian measure?
Holt Algebra The Unit Circle 13-3 The Unit Circle Holt Algebra 2 Warm Up Warm Up Lesson Presentation Lesson Presentation Lesson Quiz Lesson Quiz.
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.
Sections Perimeter and Area with Circles.
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.
© T Madas. 1 m = cm cm = mm 10 1 km = m m = cm cm = mm 40 3 km = m m = cm cm = mm km = m cm = m 4 80.
Mathematic Skills 1. Determine - area of sector radius - the radius - the angle subtended center of a circle 2. Find the area of segment of circle Prior.
4.1 Radian and Degree measure Changing Degrees to Radians Linear speed Angular speed.
1 INTERESTING CANCELLING. 2 LIMITS OF TRIGONOMETRIC FUNCTIONS In order to understand the derivatives that the trigonometric functions will produce, we.
Try describing the angle of the shaded areas without using degrees.
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.
Accelerated Math 2. Two minor arcs are congruent if and only if their corresponding chords are congruent.
Objective: To find the areas of circles, sectors and segments of circles.
Circles…… Area and Circumference The Circumference of a Circle Find the circumference of the following circles. C = d C = 2 r 8 cm cm 2 C =
The Unit Circle PreCalculus. Right now… Get a protractor, scissors, and one copy of each circle (blue, green, yellow, white). Sit down and take everything.
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.
Radian Measure. What is to be learned What a radian is How to convert between radians and degrees.
Higher Mathematics Unit 1 Trigonometric Functions and Graphs.
Special Right Triangles Isosceles Right Triangles 45 –
Measuring Arcs and Central Angles. Measuring Arcs Arcs can be measured in two ways, by their length, or by degree For now, we will be measuring arcs only.
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.
Copyright © 2013, 2009, 2005 Pearson Education, Inc. 1 3 Radian Measure and the Unit Circle Copyright © 2013, 2009, 2005 Pearson Education, Inc. 1.
Side Relationships in Special Right Triangles & Exact Values of The Trigonometric Functions.
Copyright © 2011 Pearson Education, Inc. Radian Measure, Arc Length, and Area Section 1.2 Angles and the Trigonometric Functions.
IB Revision Lesson 2 30 ° 45 °60° sin θ cos θ tan θ
3 Radian Measure and Circular Functions © 2008 Pearson Addison-Wesley. All rights reserved.
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.
Applications of Radian Measure Trigonometry Section 3.2.
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)
And because we are dealing with the unit circle here, we can say that for this special case, Remember:
RADIANS Radians, like degrees, are a way of measuring angles.
Circumference & Arc Length. Circumference The distance around a circle C = 2r or d.
Special Shortcuts for and Triangles.
Hepatitis B Virus. Hepatitis B - Clinical Features Incubation period:Average days Range days Clinical illness (jaundice):<5 yrs, <10% 5.
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.
Pulleys at an Angle. FBD-S m 1 = 100 kg m 2 = 300 kg 30° vivi 0 t10 s θ30° µ0 m1m1 100 kg m2m2 300 kg No Friction.
Special Right Triangles 1 G.8.2 Special Right Triangles.
Lesson 7-3: Special Right Triangles 1 Lesson 7-3 Special Right Triangles.
7-2 Sectors of Circles Objective: To find the arc length of a sector of a circle and to solve problems involving apparent size.
Copyright © 2003 Pearson Education, Inc. Slide Radian Measure, Arc Length, and Area Another way to measure angles is using what is called radians.
Copyright © Cengage Learning. All rights reserved. 4.4 Trigonometric Functions of Any Angle.
TrigonometryLaw of Sines Law of Sines: sin A sin B sin C (derived from the new area formula) abc Proof: b a c B AC Problems: x 60° 76 x 45° 8 60°
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.
+ What is a RADIAN?!?!. + ♪♪ Twinkle Twinkle Little Star Circumference Equals 2πr ♪♪ Length of an arc (Arc Length): s = r θ s = (πr θ )/180 1 Revolution.
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