11 x1 t04 01 trigonometric ratios (2012)

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Trigonometric Ratios

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Page 1: 11 x1 t04 01 trigonometric ratios (2012)

Trigonometric Ratios

Page 2: 11 x1 t04 01 trigonometric ratios (2012)

Trigonometric Ratios hypotenuse

adjacent

opposite

Page 3: 11 x1 t04 01 trigonometric ratios (2012)

Trigonometric Ratios hypotenuse

sin opphyp

adjacent

opposite

cos adjhyp

tan oppadj

Page 4: 11 x1 t04 01 trigonometric ratios (2012)

Trigonometric Ratios hypotenuse

sin opphyp

adjacent

opposite

cos adjhyp

tan oppadj

cosec hypopp

sec hypadj

cot adjopp

Page 5: 11 x1 t04 01 trigonometric ratios (2012)

Trigonometric Ratios hypotenuse

sin opphyp

adjacent

opposite

cos adjhyp

tan oppadj

cosec hypopp

sec hypadj

cot adjopp

e.g. sin cos 25i x

Page 6: 11 x1 t04 01 trigonometric ratios (2012)

Trigonometric Ratios hypotenuse

sin opphyp

adjacent

opposite

cos adjhyp

tan oppadj

cosec hypopp

sec hypadj

cot adjopp

e.g. sin cos 25i x

90 25x 65x

Page 7: 11 x1 t04 01 trigonometric ratios (2012)

Trigonometric Ratios hypotenuse

sin opphyp

adjacent

opposite

cos adjhyp

tan oppadj

cosec hypopp

sec hypadj

cot adjopp

e.g. sin cos25i x

90 25x 65x

cot 20 tan 30ii x x

Page 8: 11 x1 t04 01 trigonometric ratios (2012)

Trigonometric Ratios hypotenuse

sin opphyp

adjacent

opposite

cos adjhyp

tan oppadj

cosec hypopp

sec hypadj

cot adjopp

e.g. sin cos25i x

90 25x 65x

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

2 8040

xx

Page 9: 11 x1 t04 01 trigonometric ratios (2012)

iii

a

1361

Page 10: 11 x1 t04 01 trigonometric ratios (2012)

iii

a

1361

tan 6113a

Page 11: 11 x1 t04 01 trigonometric ratios (2012)

iii

a

1361

tan 6113a

13tan 61a

23.5 units (to 1 dp)a

Page 12: 11 x1 t04 01 trigonometric ratios (2012)

iii

a

1361

tan 6113a

13tan 61a

23.5 units (to 1 dp)a

iv

x

5

32

Page 13: 11 x1 t04 01 trigonometric ratios (2012)

iii

a

1361

tan 6113a

13tan 61a

23.5 units (to 1 dp)a

iv

x

5

32

5 sin32x

Page 14: 11 x1 t04 01 trigonometric ratios (2012)

iii

a

1361

tan 6113a

13tan 61a

23.5 units (to 1 dp)a

iv

x

5

32

5 sin32x

5sin32

x

9.4 units (to 1 dp)x

Page 15: 11 x1 t04 01 trigonometric ratios (2012)

iii

a

1361

tan 6113a

13tan 61a

23.5 units (to 1 dp)a

iv

x

5

32

5 sin32x

5sin32

x

9.4 units (to 1 dp)x

v

10

14

Page 16: 11 x1 t04 01 trigonometric ratios (2012)

iii

a

1361

tan 6113a

13tan 61a

23.5 units (to 1 dp)a

iv

x

5

32

5 sin32x

5sin32

x

9.4 units (to 1 dp)x

v

10

14

10cos14

Page 17: 11 x1 t04 01 trigonometric ratios (2012)

iii

a

1361

tan 6113a

13tan 61a

23.5 units (to 1 dp)a

iv

x

5

32

5 sin32x

5sin32

x

9.4 units (to 1 dp)x

v

10

14

10cos14

1 10cos14

44 25

Page 18: 11 x1 t04 01 trigonometric ratios (2012)

Exact Ratios

60

60

60

Page 19: 11 x1 t04 01 trigonometric ratios (2012)

Exact Ratios

22

260

60

60

Page 20: 11 x1 t04 01 trigonometric ratios (2012)

Exact Ratios

2

160

303

Page 21: 11 x1 t04 01 trigonometric ratios (2012)

Exact Ratios

2

160

303

1sin302

3cos302

1tan303

Page 22: 11 x1 t04 01 trigonometric ratios (2012)

Exact Ratios

2

160

303

1sin302

3cos302

1tan303

3sin 602

1cos602

tan 60 3

Page 23: 11 x1 t04 01 trigonometric ratios (2012)

Exact Ratios

2

160

303

1sin302

3cos302

1tan303

3sin 602

1cos602

tan 60 3

45

451

12

Page 24: 11 x1 t04 01 trigonometric ratios (2012)

Exact Ratios

2

160

303

1sin302

3cos302

1tan303

3sin 602

1cos602

tan 60 3

45

451

12

1sin 452

1cos 452

tan 45 1

Page 25: 11 x1 t04 01 trigonometric ratios (2012)

Alternative way of remembering the exact ratios

sin

cos

tan

0 30 45 60 90

Page 26: 11 x1 t04 01 trigonometric ratios (2012)

Alternative way of remembering the exact ratios

sin

cos

tan

0 30 45 60 90

02

12

22

32

42

Page 27: 11 x1 t04 01 trigonometric ratios (2012)

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

Page 28: 11 x1 t04 01 trigonometric ratios (2012)

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

Page 29: 11 x1 t04 01 trigonometric ratios (2012)

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

Page 30: 11 x1 t04 01 trigonometric ratios (2012)

Measuring Angles

Page 31: 11 x1 t04 01 trigonometric ratios (2012)

Measuring AnglesAngle of Elevation

A

B

Page 32: 11 x1 t04 01 trigonometric ratios (2012)

Measuring AnglesAngle of Elevation

A

B

angle of elevation of B from A

Page 33: 11 x1 t04 01 trigonometric ratios (2012)

Measuring AnglesAngle of Elevation

A

B

angle of elevation of B from A

Angle of Depression

X

Y

Page 34: 11 x1 t04 01 trigonometric ratios (2012)

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

Page 35: 11 x1 t04 01 trigonometric ratios (2012)

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

Page 36: 11 x1 t04 01 trigonometric ratios (2012)

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

Page 37: 11 x1 t04 01 trigonometric ratios (2012)

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

Page 38: 11 x1 t04 01 trigonometric ratios (2012)

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

Page 39: 11 x1 t04 01 trigonometric ratios (2012)

True BearingsAlways start NORTH and measure clockwise

Page 40: 11 x1 t04 01 trigonometric ratios (2012)

True BearingsAlways start NORTH and measure clockwise

X

Y

Page 41: 11 x1 t04 01 trigonometric ratios (2012)

True BearingsAlways start NORTH and measure clockwise

X

Y

Bearing of Y from X

Page 42: 11 x1 t04 01 trigonometric ratios (2012)

True BearingsAlways start NORTH and measure clockwise

N

X

Y

30

Bearing of Y from X

Page 43: 11 x1 t04 01 trigonometric ratios (2012)

True BearingsAlways start NORTH and measure clockwise

N

X

Y

30

Bearing of Y from X120 T

or S60 E

Page 44: 11 x1 t04 01 trigonometric ratios (2012)

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

Page 45: 11 x1 t04 01 trigonometric ratios (2012)

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

Page 46: 11 x1 t04 01 trigonometric ratios (2012)

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

Page 47: 11 x1 t04 01 trigonometric ratios (2012)

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