12 x1 t03 01 arcs & sectors (2012)

27
Trigonometric Functions

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Page 1: 12 x1 t03 01 arcs & sectors (2012)

Trigonometric Functions

Page 2: 12 x1 t03 01 arcs & sectors (2012)

Trigonometric Functionsradians2360

Page 3: 12 x1 t03 01 arcs & sectors (2012)

Trigonometric Functionsradians2360

Arcs & Sectors

Page 4: 12 x1 t03 01 arcs & sectors (2012)

Trigonometric Functionsradians2360

rC 2

Arcs & Sectors

Page 5: 12 x1 t03 01 arcs & sectors (2012)

Trigonometric Functionsradians2360

rC 2 2rA

Arcs & Sectors

Page 6: 12 x1 t03 01 arcs & sectors (2012)

Trigonometric Functionsradians2360

rC 2 2rA

Arcs & SectorsO

A

B

Page 7: 12 x1 t03 01 arcs & sectors (2012)

Trigonometric Functionsradians2360

rC 2 2rA

Arcs & SectorsO

A

B

AB is an arc

Page 8: 12 x1 t03 01 arcs & sectors (2012)

Trigonometric Functionsradians2360

rC 2 2rA

Arcs & SectorsO

A

B

AB is an arc

l

Page 9: 12 x1 t03 01 arcs & sectors (2012)

Trigonometric Functionsradians2360

rC 2 2rA

Arcs & SectorsO

A

B

AB is an arc

lrl

22

Page 10: 12 x1 t03 01 arcs & sectors (2012)

Trigonometric Functionsradians2360

rC 2 2rA

Arcs & SectorsO

A

B

AB is an arc

lrl

22

rl

Page 11: 12 x1 t03 01 arcs & sectors (2012)

Trigonometric Functionsradians2360

rC 2 2rA

Arcs & SectorsO

A

B

AB is an arc

lrl

22

rl

Length of an arc; rl

Page 12: 12 x1 t03 01 arcs & sectors (2012)

Trigonometric Functionsradians2360

rC 2 2rA

Arcs & SectorsO

A

B

OAB is a sector

AB is an arc

lrl

22

rl

Length of an arc; rl

Page 13: 12 x1 t03 01 arcs & sectors (2012)

Trigonometric Functionsradians2360

rC 2 2rA

Arcs & SectorsO

A

B

OAB is a sector

AB is an arc

lrl

22

rl

2

2rAOAB

Length of an arc; rl

Page 14: 12 x1 t03 01 arcs & sectors (2012)

Trigonometric Functionsradians2360

rC 2 2rA

Arcs & SectorsO

A

B

OAB is a sector

AB is an arc

lrl

22

rl

2

2rAOAB

221 rAOAB

Length of an arc; rl

Page 15: 12 x1 t03 01 arcs & sectors (2012)

Trigonometric Functionsradians2360

rC 2 2rA

Arcs & SectorsO

A

B

OAB is a sector

AB is an arc

lrl

22

rl

2

2rAOAB

221 rAOAB

Length of an arc; rl

Area of a sector; 221 rA

Page 16: 12 x1 t03 01 arcs & sectors (2012)

45

e.g.

O

A

B5

cm

Page 17: 12 x1 t03 01 arcs & sectors (2012)

45

rlAB e.g.

O

A

B5

cm

Page 18: 12 x1 t03 01 arcs & sectors (2012)

rlAB e.g.

45

45O

A

B5

cm

Page 19: 12 x1 t03 01 arcs & sectors (2012)

rlAB e.g.

45

cm 4

5

45O

A

B5

cm

Page 20: 12 x1 t03 01 arcs & sectors (2012)

rlAB 221 rAOAB

e.g.

45

cm 4

5

45O

A

B5

cm

Page 21: 12 x1 t03 01 arcs & sectors (2012)

rlAB 221 rAOAB

e.g.

45

cm 4

5

45

21 2

45O

A

B5

cm

Page 22: 12 x1 t03 01 arcs & sectors (2012)

rlAB 221 rAOAB

e.g.

45

cm 4

5

45

21 2

2cm 8

25

45O

A

B5

cm

Page 23: 12 x1 t03 01 arcs & sectors (2012)

45

rlAB 221 rAOAB

ABsegmentminor Area

e.g.

O

A

B5

cm

45

cm 4

5

45

21 2

2cm 8

25

Page 24: 12 x1 t03 01 arcs & sectors (2012)

45

rlAB 221 rAOAB

ABsegmentminor Area

sin21

sin21

21

2

22

r

rr

e.g.

O

A

B5

cm

45

cm 4

5

45

21 2

2cm 8

25

Page 25: 12 x1 t03 01 arcs & sectors (2012)

45

rlAB 221 rAOAB

ABsegmentminor Area

sin21

sin21

21

2

22

r

rr

e.g.

O

A

B5

cm

45

cm 4

5

45

21 2

2cm 8

25

Page 26: 12 x1 t03 01 arcs & sectors (2012)

45

rlAB 221 rAOAB

ABsegmentminor Area

sin21

sin21

21

2

22

r

rr

2

2

cm 28

1002252

142

254

sin4

521

e.g.

O

A

B5

cm

45

cm 4

5

45

21 2

2cm 8

25

Page 27: 12 x1 t03 01 arcs & sectors (2012)

45

rlAB 221 rAOAB

ABsegmentminor Area

sin21

sin21

21

2

22

r

rr

2

2

cm 28

1002252

142

254

sin4

521

e.g.

O

A

B5

cm

45

cm 4

5

45

21 2

2cm 8

25

Exercise 14B; 2 to 24 evens, 25, 28*