SlideShare una empresa de Scribd logo
1 de 7
Descargar para leer sin conexión
Unit Circle / Circular Functions



                 terminal
                 arm/ side
                                            initial arm/ side




Let the terminal arm be "r" = 1 and rotate it once,
this results in a circle with a radius = 1 unit in length,
   Unit Circle



    Standard Position of
                                    Initial arm lays
                                    on the x-axis


                                    the origin
Coterminal Angles
angles which share the same terminal side/ arm




ex. Give two coterminal angles for 30
Measurement of Angles
                             3 Systems

               - unit symbol is
                         o


               - has no unit symbol

                             r
                        s-
                 ra diu




                                 = arc length = s




The central angle is subtended or "covered" by an arc length
(for a given radius)

1 revolution (once around) = 360

 C=2     r


 in rads =                       rads or radians
                      or 2 (3.14) = 6.28 rads
The Connection -> Rads to Degrees




Degrees           Radians
                (exact values)
Converting Degrees          Radians

Recall




ex 1) How many radian is

               (in   -terms)
ex 2) How many degrees is

Más contenido relacionado

La actualidad más candente

media tiga dimensi
media tiga dimensimedia tiga dimensi
media tiga dimensiRSA1C314014
 
Lect12 handout
Lect12 handoutLect12 handout
Lect12 handoutnomio0703
 
Trusses Joints 2
Trusses Joints 2Trusses Joints 2
Trusses Joints 2Amr Hamed
 
Shear and Bending Moment in Beams
Shear and Bending Moment in BeamsShear and Bending Moment in Beams
Shear and Bending Moment in BeamsAmr Hamed
 
Standing waves lo
Standing waves loStanding waves lo
Standing waves loChris Cheng
 
Shear force and bending moment
Shear force and bending momentShear force and bending moment
Shear force and bending momenttalha022
 
Pure bending of curved bar (polar coordinate)
 Pure bending of curved bar (polar coordinate) Pure bending of curved bar (polar coordinate)
Pure bending of curved bar (polar coordinate)Pratish Sardar
 
Structure Design-I (Bending moment & Shear force Part II)
Structure Design-I (Bending moment & Shear force Part II)Structure Design-I (Bending moment & Shear force Part II)
Structure Design-I (Bending moment & Shear force Part II)Simran Vats
 
FLEXURAL STRESSES AND SHEAR STRESSES
FLEXURAL STRESSES AND SHEAR STRESSESFLEXURAL STRESSES AND SHEAR STRESSES
FLEXURAL STRESSES AND SHEAR STRESSESvempatishiva
 
10-7 Areas of Circles and Sectors
10-7 Areas of Circles and Sectors10-7 Areas of Circles and Sectors
10-7 Areas of Circles and Sectorsjtentinger
 
Sfd and bmd engineering science n4
Sfd and bmd engineering science n4Sfd and bmd engineering science n4
Sfd and bmd engineering science n4Jude Jay
 
6161103 3.3 coplanar systems
6161103 3.3 coplanar systems6161103 3.3 coplanar systems
6161103 3.3 coplanar systemsetcenterrbru
 
Physics 101 learning objective 2
Physics 101 learning objective 2Physics 101 learning objective 2
Physics 101 learning objective 2jeffer7
 

La actualidad más candente (20)

media tiga dimensi
media tiga dimensimedia tiga dimensi
media tiga dimensi
 
Lect12 handout
Lect12 handoutLect12 handout
Lect12 handout
 
Trusses Joints 2
Trusses Joints 2Trusses Joints 2
Trusses Joints 2
 
Shear and Bending Moment in Beams
Shear and Bending Moment in BeamsShear and Bending Moment in Beams
Shear and Bending Moment in Beams
 
Sfd bmd
Sfd  bmdSfd  bmd
Sfd bmd
 
Standing waves lo
Standing waves loStanding waves lo
Standing waves lo
 
Shear force and bending moment
Shear force and bending momentShear force and bending moment
Shear force and bending moment
 
Resistor combinations
Resistor combinationsResistor combinations
Resistor combinations
 
Pure bending of curved bar (polar coordinate)
 Pure bending of curved bar (polar coordinate) Pure bending of curved bar (polar coordinate)
Pure bending of curved bar (polar coordinate)
 
Structure Design-I (Bending moment & Shear force Part II)
Structure Design-I (Bending moment & Shear force Part II)Structure Design-I (Bending moment & Shear force Part II)
Structure Design-I (Bending moment & Shear force Part II)
 
FLEXURAL STRESSES AND SHEAR STRESSES
FLEXURAL STRESSES AND SHEAR STRESSESFLEXURAL STRESSES AND SHEAR STRESSES
FLEXURAL STRESSES AND SHEAR STRESSES
 
10-7 Areas of Circles and Sectors
10-7 Areas of Circles and Sectors10-7 Areas of Circles and Sectors
10-7 Areas of Circles and Sectors
 
Columns
ColumnsColumns
Columns
 
Sfd and bmd engineering science n4
Sfd and bmd engineering science n4Sfd and bmd engineering science n4
Sfd and bmd engineering science n4
 
6161103 3.3 coplanar systems
6161103 3.3 coplanar systems6161103 3.3 coplanar systems
6161103 3.3 coplanar systems
 
Physics 17-2
Physics 17-2Physics 17-2
Physics 17-2
 
Shear stresses in beams
Shear stresses in beamsShear stresses in beams
Shear stresses in beams
 
Physics 101 learning objective 2
Physics 101 learning objective 2Physics 101 learning objective 2
Physics 101 learning objective 2
 
Shear Force
Shear ForceShear Force
Shear Force
 
The RC Circuit
The RC CircuitThe RC Circuit
The RC Circuit
 

Destacado (13)

Day 3 examples
Day 3 examplesDay 3 examples
Day 3 examples
 
Day 1 examples
Day 1 examplesDay 1 examples
Day 1 examples
 
Day 5 examples
Day 5 examplesDay 5 examples
Day 5 examples
 
Day 2 examples
Day 2 examplesDay 2 examples
Day 2 examples
 
Day 4 examples
Day 4 examplesDay 4 examples
Day 4 examples
 
Day 3 examples
Day 3 examplesDay 3 examples
Day 3 examples
 
Day 4 examples
Day 4 examplesDay 4 examples
Day 4 examples
 
Day 2 examples
Day 2 examplesDay 2 examples
Day 2 examples
 
Day 3 examples
Day 3 examplesDay 3 examples
Day 3 examples
 
Day 4 examples
Day 4 examplesDay 4 examples
Day 4 examples
 
Day 6 examples
Day 6 examplesDay 6 examples
Day 6 examples
 
Day 8 examples
Day 8 examplesDay 8 examples
Day 8 examples
 
Day 7 examples
Day 7 examplesDay 7 examples
Day 7 examples
 

Similar a Unit Circle Circular Functions

4.1A Angles and Angle Measure.pptx
4.1A Angles and Angle Measure.pptx4.1A Angles and Angle Measure.pptx
4.1A Angles and Angle Measure.pptxRoyCatampongan1
 
scueeeeerrrre.pptxjjsbshjdjjrhdhbhhhggggg
scueeeeerrrre.pptxjjsbshjdjjrhdhbhhhgggggscueeeeerrrre.pptxjjsbshjdjjrhdhbhhhggggg
scueeeeerrrre.pptxjjsbshjdjjrhdhbhhhgggggRoyCatampongan1
 
Measurfe.pptxddfsfdfferosddodddfwwffffffff
Measurfe.pptxddfsfdfferosddodddfwwffffffffMeasurfe.pptxddfsfdfferosddodddfwwffffffff
Measurfe.pptxddfsfdfferosddodddfwwffffffffRoyCatampongan1
 
4.1A Angles and Angle Measure.pptx
4.1A Angles and Angle Measure.pptx4.1A Angles and Angle Measure.pptx
4.1A Angles and Angle Measure.pptxarvin gutierrez
 
Appendex a
Appendex aAppendex a
Appendex aswavicky
 
Radians, arc length and sector area
Radians, arc length and sector areaRadians, arc length and sector area
Radians, arc length and sector areaJJkedst
 
PC_Q2_W1-2_Angles in a Unit Circle Presentation PPT
PC_Q2_W1-2_Angles in a Unit Circle Presentation PPTPC_Q2_W1-2_Angles in a Unit Circle Presentation PPT
PC_Q2_W1-2_Angles in a Unit Circle Presentation PPTRichieReyes12
 
Trigonometry For
Trigonometry ForTrigonometry For
Trigonometry Fordaisyrock
 
Antenna basicsmods1&2
Antenna basicsmods1&2Antenna basicsmods1&2
Antenna basicsmods1&2Mano Devaraj
 
PM [B05] Angles & Measurement
PM [B05] Angles & MeasurementPM [B05] Angles & Measurement
PM [B05] Angles & MeasurementStephen Kwong
 
A quick review of trignometery
A quick review of trignometeryA quick review of trignometery
A quick review of trignometeryTarun Gehlot
 
6.1 Radian Measure
6.1 Radian Measure6.1 Radian Measure
6.1 Radian Measuresmiller5
 
Antenna and Wave Propagation.pdf
Antenna and Wave Propagation.pdfAntenna and Wave Propagation.pdf
Antenna and Wave Propagation.pdfJohnColaco1
 

Similar a Unit Circle Circular Functions (20)

4.1A Angles and Angle Measure.pptx
4.1A Angles and Angle Measure.pptx4.1A Angles and Angle Measure.pptx
4.1A Angles and Angle Measure.pptx
 
scueeeeerrrre.pptxjjsbshjdjjrhdhbhhhggggg
scueeeeerrrre.pptxjjsbshjdjjrhdhbhhhgggggscueeeeerrrre.pptxjjsbshjdjjrhdhbhhhggggg
scueeeeerrrre.pptxjjsbshjdjjrhdhbhhhggggg
 
Measurfe.pptxddfsfdfferosddodddfwwffffffff
Measurfe.pptxddfsfdfferosddodddfwwffffffffMeasurfe.pptxddfsfdfferosddodddfwwffffffff
Measurfe.pptxddfsfdfferosddodddfwwffffffff
 
math 10
math 10math 10
math 10
 
4.1A Angles and Angle Measure.pptx
4.1A Angles and Angle Measure.pptx4.1A Angles and Angle Measure.pptx
4.1A Angles and Angle Measure.pptx
 
Trignometryppt
TrignometrypptTrignometryppt
Trignometryppt
 
Appendex a
Appendex aAppendex a
Appendex a
 
Radians, arc length and sector area
Radians, arc length and sector areaRadians, arc length and sector area
Radians, arc length and sector area
 
PC_Q2_W1-2_Angles in a Unit Circle Presentation PPT
PC_Q2_W1-2_Angles in a Unit Circle Presentation PPTPC_Q2_W1-2_Angles in a Unit Circle Presentation PPT
PC_Q2_W1-2_Angles in a Unit Circle Presentation PPT
 
Trigonometry For
Trigonometry ForTrigonometry For
Trigonometry For
 
Circle - arc sector
Circle  - arc sectorCircle  - arc sector
Circle - arc sector
 
Survey 2 curves1
Survey 2 curves1Survey 2 curves1
Survey 2 curves1
 
Antenna basicsmods1&2
Antenna basicsmods1&2Antenna basicsmods1&2
Antenna basicsmods1&2
 
Trigonometry
TrigonometryTrigonometry
Trigonometry
 
Trigonometry
TrigonometryTrigonometry
Trigonometry
 
PM [B05] Angles & Measurement
PM [B05] Angles & MeasurementPM [B05] Angles & Measurement
PM [B05] Angles & Measurement
 
A quick review of trignometery
A quick review of trignometeryA quick review of trignometery
A quick review of trignometery
 
6.1 Radian Measure
6.1 Radian Measure6.1 Radian Measure
6.1 Radian Measure
 
Antenna and Wave Propagation.pdf
Antenna and Wave Propagation.pdfAntenna and Wave Propagation.pdf
Antenna and Wave Propagation.pdf
 
ARS 01.01.pptx
ARS 01.01.pptxARS 01.01.pptx
ARS 01.01.pptx
 

Más de jchartiersjsd

Combs perms review pascals
Combs perms review pascalsCombs perms review pascals
Combs perms review pascalsjchartiersjsd
 
Day 8 examples u7w14
Day 8 examples u7w14Day 8 examples u7w14
Day 8 examples u7w14jchartiersjsd
 
Day 7 examples u7w14
Day 7 examples u7w14Day 7 examples u7w14
Day 7 examples u7w14jchartiersjsd
 
Day 4 examples u7w14
Day 4 examples u7w14Day 4 examples u7w14
Day 4 examples u7w14jchartiersjsd
 
Day 3 examples u7w14
Day 3 examples u7w14Day 3 examples u7w14
Day 3 examples u7w14jchartiersjsd
 
Day 2 examples u7w14
Day 2 examples u7w14Day 2 examples u7w14
Day 2 examples u7w14jchartiersjsd
 
Day 1 examples u7w14
Day 1 examples u7w14Day 1 examples u7w14
Day 1 examples u7w14jchartiersjsd
 
Test outline comp rational
Test outline comp rationalTest outline comp rational
Test outline comp rationaljchartiersjsd
 
Day 7 examples u6w14
Day 7 examples u6w14Day 7 examples u6w14
Day 7 examples u6w14jchartiersjsd
 
Day 5 examples u6w14
Day 5 examples u6w14Day 5 examples u6w14
Day 5 examples u6w14jchartiersjsd
 
Day 4 examples u6w14
Day 4 examples u6w14Day 4 examples u6w14
Day 4 examples u6w14jchartiersjsd
 
Day 3 examples u6w14
Day 3 examples u6w14Day 3 examples u6w14
Day 3 examples u6w14jchartiersjsd
 
Day 2 examples u6w14
Day 2 examples u6w14Day 2 examples u6w14
Day 2 examples u6w14jchartiersjsd
 
Day 1 examples u6w14
Day 1 examples u6w14Day 1 examples u6w14
Day 1 examples u6w14jchartiersjsd
 
Mental math test outline
Mental math test outlineMental math test outline
Mental math test outlinejchartiersjsd
 
Day 8 examples u5w14
Day 8 examples u5w14Day 8 examples u5w14
Day 8 examples u5w14jchartiersjsd
 
Day 7 examples u5w14
Day 7 examples u5w14Day 7 examples u5w14
Day 7 examples u5w14jchartiersjsd
 
Day 5 examples u5w14
Day 5 examples u5w14Day 5 examples u5w14
Day 5 examples u5w14jchartiersjsd
 

Más de jchartiersjsd (20)

Exam outline j14
Exam outline j14Exam outline j14
Exam outline j14
 
Test outline
Test outlineTest outline
Test outline
 
Combs perms review pascals
Combs perms review pascalsCombs perms review pascals
Combs perms review pascals
 
Day 8 examples u7w14
Day 8 examples u7w14Day 8 examples u7w14
Day 8 examples u7w14
 
Day 7 examples u7w14
Day 7 examples u7w14Day 7 examples u7w14
Day 7 examples u7w14
 
Day 4 examples u7w14
Day 4 examples u7w14Day 4 examples u7w14
Day 4 examples u7w14
 
Day 3 examples u7w14
Day 3 examples u7w14Day 3 examples u7w14
Day 3 examples u7w14
 
Day 2 examples u7w14
Day 2 examples u7w14Day 2 examples u7w14
Day 2 examples u7w14
 
Day 1 examples u7w14
Day 1 examples u7w14Day 1 examples u7w14
Day 1 examples u7w14
 
Test outline comp rational
Test outline comp rationalTest outline comp rational
Test outline comp rational
 
Day 7 examples u6w14
Day 7 examples u6w14Day 7 examples u6w14
Day 7 examples u6w14
 
Day 5 examples u6w14
Day 5 examples u6w14Day 5 examples u6w14
Day 5 examples u6w14
 
Day 4 examples u6w14
Day 4 examples u6w14Day 4 examples u6w14
Day 4 examples u6w14
 
Day 3 examples u6w14
Day 3 examples u6w14Day 3 examples u6w14
Day 3 examples u6w14
 
Day 2 examples u6w14
Day 2 examples u6w14Day 2 examples u6w14
Day 2 examples u6w14
 
Day 1 examples u6w14
Day 1 examples u6w14Day 1 examples u6w14
Day 1 examples u6w14
 
Mental math test outline
Mental math test outlineMental math test outline
Mental math test outline
 
Day 8 examples u5w14
Day 8 examples u5w14Day 8 examples u5w14
Day 8 examples u5w14
 
Day 7 examples u5w14
Day 7 examples u5w14Day 7 examples u5w14
Day 7 examples u5w14
 
Day 5 examples u5w14
Day 5 examples u5w14Day 5 examples u5w14
Day 5 examples u5w14
 

Unit Circle Circular Functions

  • 1. Unit Circle / Circular Functions terminal arm/ side initial arm/ side Let the terminal arm be "r" = 1 and rotate it once, this results in a circle with a radius = 1 unit in length, Unit Circle Standard Position of Initial arm lays on the x-axis the origin
  • 2.
  • 3. Coterminal Angles angles which share the same terminal side/ arm ex. Give two coterminal angles for 30
  • 4. Measurement of Angles 3 Systems - unit symbol is o - has no unit symbol r s- ra diu = arc length = s The central angle is subtended or "covered" by an arc length (for a given radius) 1 revolution (once around) = 360 C=2 r in rads = rads or radians or 2 (3.14) = 6.28 rads
  • 5. The Connection -> Rads to Degrees Degrees Radians (exact values)
  • 6. Converting Degrees Radians Recall ex 1) How many radian is (in -terms)
  • 7. ex 2) How many degrees is