11X1 T04 01 trig ratios

Download 11X1 T04 01 trig ratios

Post on 17-Jul-2015

388 views

Category:

Education

2 download

TRANSCRIPT

  • Trigonometric Ratios

  • Trigonometric Ratios hypotenuse

    adjacent

    opposite

  • Trigonometric Ratios hypotenuse

    sin opphyp

    adjacent

    opposite

    cos adjhyp

    tan oppadj

  • Trigonometric Ratios hypotenuse

    sin opphyp

    adjacent

    opposite

    cos adjhyp

    tan oppadj

    cosec hypopp

    sec hyp

    adj

    cot adjopp

  • Trigonometric Ratios hypotenuse

    sin opphyp

    adjacent

    opposite

    cos adjhyp

    tan oppadj

    cosec hypopp

    sec hyp

    adj

    cot adjopp

    e.g. sin cos 25i x

  • Trigonometric Ratios hypotenuse

    sin opphyp

    adjacent

    opposite

    cos adjhyp

    tan oppadj

    cosec hypopp

    sec hyp

    adj

    cot adjopp

    e.g. sin cos 25i x 90 25x 65x

  • Trigonometric Ratios hypotenuse

    sin opphyp

    adjacent

    opposite

    cos adjhyp

    tan oppadj

    cosec hypopp

    sec hyp

    adj

    cot adjopp

    e.g. sin cos25i x 90 25x 65x

    cot 20 tan 30ii x x

  • Trigonometric Ratios hypotenuse

    sin opphyp

    adjacent

    opposite

    cos adjhyp

    tan oppadj

    cosec hypopp

    sec hyp

    adj

    cot adjopp

    e.g. sin cos25i x 90 25x 65x

    cot 20 tan 30ii x x 20 30 90x x

    2 8040

    xx

  • iiia

    1361

  • iiia

    1361

    tan 6113a

  • iiia

    1361

    tan 6113a

    13tan 61a 23.5 units (to 1 dp)a

  • iiia

    1361

    tan 6113a

    13tan 61a 23.5 units (to 1 dp)a

    ivx

    5

    32

  • iiia

    1361

    tan 6113a

    13tan 61a 23.5 units (to 1 dp)a

    ivx

    5

    32

    5 sin32x

  • iiia

    1361

    tan 6113a

    13tan 61a 23.5 units (to 1 dp)a

    ivx

    5

    32

    5 sin32x

    5sin32

    x 9.4 units (to 1 dp)x

  • iiia

    1361

    tan 6113a

    13tan 61a 23.5 units (to 1 dp)a

    ivx

    5

    32

    5 sin32x

    5sin32

    x 9.4 units (to 1 dp)x

    v

    10

    14

  • iiia

    1361

    tan 6113a

    13tan 61a 23.5 units (to 1 dp)a

    ivx

    5

    32

    5 sin32x

    5sin32

    x 9.4 units (to 1 dp)x

    v

    10

    14

    10cos14

  • iiia

    1361

    tan 6113a

    13tan 61a 23.5 units (to 1 dp)a

    ivx

    5

    32

    5 sin32x

    5sin32

    x 9.4 units (to 1 dp)x

    v

    10

    14

    10cos14

    1 10cos14

    44 25

  • Exact Ratios

    60

    60

    60

  • Exact Ratios

    22

    260

    60

    60

  • Exact Ratios

    2

    160

    303

  • Exact Ratios

    2

    160

    303

    1sin302

    3cos302

    1tan303

  • Exact Ratios

    2

    160

    303

    1sin302

    3cos302

    1tan303

    3sin 602

    1cos602

    tan 60 3

  • Exact Ratios

    2

    160

    303

    1sin302

    3cos302

    1tan303

    3sin 602

    1cos602

    tan 60 3

    45

    451

    12

  • Exact Ratios

    2

    160

    303

    1sin302

    3cos302

    1tan303

    3sin 602

    1cos602

    tan 60 3

    45

    451

    12

    1sin 452

    1cos 452

    tan 45 1

  • Alternative way of remembering the exact ratios

    sin

    cos

    tan

    0 30 45 60 90

  • Alternative way of remembering the exact ratios

    sin

    cos

    tan

    0 30 45 60 90

    02

    12

    22

    32

    42

  • Alternative way of remembering the exact ratios

    sin

    cos

    tan

    0 30 45 60 90

    02

    12

    22

    32

    42

    42

    32

    22

    12

    02

  • Alternative way of remembering the exact ratios

    sin

    cos

    tan

    0 30 45 60 90

    02

    12

    22

    32

    42

    42

    32

    22

    12

    02

    sincos

  • Alternative way of remembering the exact ratios

    sin

    cos

    tan

    0 30 45 60 90

    02

    12

    22

    32

    42

    42

    32

    22

    12

    02

    sincos

    04

    13

    22

    31

    40

  • Measuring Angles

  • Measuring AnglesAngle of Elevation

    A

    B

  • Measuring AnglesAngle of Elevation

    A

    B

    angle of elevation of B from A

  • Measuring AnglesAngle of Elevation

    A

    B

    angle of elevation of B from A

    Angle of Depression

    X

    Y

  • Measuring AnglesAngle of Elevation

    A

    B

    angle of elevation of B from A

    Angle of Depression

    X

    Y

    angle of depresion of X from Y

  • Measuring AnglesAngle of Elevation

    A

    B

    angle of elevation of B from A

    Angle of Depression

    X

    Y

    angle of depresion of X from Y

    Note: angle of elevation = angle of depression

  • Measuring AnglesAngle of Elevation

    A

    B

    angle of elevation of B from A

    Angle of Depression

    X

    Y

    angle of depresion of X from Y

    Note: angle of elevation = angle of depression

    Compass Bearings N

    S

    EW

  • Measuring AnglesAngle of Elevation

    A

    B

    angle of elevation of B from A

    Angle of Depression

    X

    Y

    angle of depresion of X from Y

    Note: angle of elevation = angle of depression

    Compass Bearings N

    S

    EW

    NE

    SESW

    NW

  • Measuring AnglesAngle of Elevation

    A

    B

    angle of elevation of B from A

    Angle of Depression

    X

    Y

    angle of depresion of X from Y

    Note: angle of elevation = angle of depression

    Compass Bearings N

    S

    EW

    NE

    SESW

    NW NNE

    ENE

    ESE

    SSESSW

    WSW

    WNW

    NNW

  • True BearingsAlways start NORTH and measure clockwise

  • True BearingsAlways start NORTH and measure clockwise

    X

    Y

  • True BearingsAlways start NORTH and measure clockwise

    X

    Y

    Bearing of Y from X

  • True BearingsAlways start NORTH and measure clockwise

    N

    X

    Y

    30

    Bearing of Y from X

  • True BearingsAlways start NORTH and measure clockwise

    N

    X

    Y

    30

    Bearing of Y from X120 T

    or S60 E

  • True BearingsAlways start NORTH and measure clockwise

    N

    X

    Y

    30

    Bearing of Y from X120 T

    or S60 E

    Bearing of X from Y

  • True BearingsAlways start NORTH and measure clockwise

    N

    X

    Y

    30

    Bearing of Y from X120 T

    or S60 E

    Bearing of X from Y

    N

    60

  • True BearingsAlways start NORTH and measure clockwise

    N

    X

    Y

    30

    Bearing of Y from X120 T

    or S60 E

    Bearing of X from Y300 T

    or N60 W

    N

    60

  • Exercise 4A; 1 to 3 (pick some), 4acf, 5, 7bd, 8ac, 9bd, 11, 12,14c, 17, 18, 19b, 21, 23, 24, 25

    Exercise 4B; 1b, 2b, 3, 4b, 6, 7, 10

    Slide Number 1Slide Number 2Slide Number 3Slide Number 4Slide Number 5Slide Number 6Slide Number 7Slide Number 8Slide Number 9Slide Number 10Slide Number 11Slide Number 12Slide Number 13Slide Number 14Slide Number 15Slide Number 16Slide Number 17Slide Number 18Slide Number 19Slide Number 20Slide Number 21Slide Number 22Slide Number 23Slide Number 24Slide Number 25Slide Number 26Slide Number 27Slide Number 28Slide Number 29Slide Number 30Slide Number 31Slide Number 32Slide Number 33Slide Number 34Slide Number 35Slide Number 36Slide Number 37Slide Number 38Slide Number 39Slide Number 40Slide Number 41Slide Number 42Slide Number 43Slide Number 44Slide Number 45Slide Number 46Slide Number 47