MATHOMAT - ERA Distributorseducation-era.com/lesson-plans/MATHOMAT_Senior_Booklet.pdf · 2015. 5....

12
Mathomat Senior has been specifically developed for Sketching and presentation of work by students from years 10 to 12. Features such as a unit circle and tangent line for trigonometry study, graphing curves and 3D soild sketch outline make Mathomat Senior an invaluable aid for projects and classwork, particularly for topis such as Trigonometry, Geometry & Measurement and Fractions & Graphs. A technical and creative drawing tool for senior secondary school students. TEMPLATE MATHOMAT SENIOR ®

Transcript of MATHOMAT - ERA Distributorseducation-era.com/lesson-plans/MATHOMAT_Senior_Booklet.pdf · 2015. 5....

Page 1: MATHOMAT - ERA Distributorseducation-era.com/lesson-plans/MATHOMAT_Senior_Booklet.pdf · 2015. 5. 24. · Mathomat Senior contains three sine/cosine curves. Each one can be used to

PO Box 6, Sandown Village, Vic, 3171, AustraliaTelephone: (03) 9796 1177 - Fax: (03) 9796 1832

www.mathomat.com.au

Published by Objective Learning Materials, a business of W&G Education Pty. Ltd. A.C.N. 051 847 637

1

Mathomat Senior has been specifically developed for Sketching andpresentation of work by students from years 10 to 12. Features such as aunit circle and tangent line for trigonometry study, graphing curves and3D soild sketch outline make Mathomat Senior an invaluable aid forprojects and classwork, particularly for topis such as Trigonometry,Geometry & Measurement and Fractions & Graphs.

A technical and creative drawing tool for senior secondary school students.

TEMPLATEMATHOMAT SENIOR

®

Page 2: MATHOMAT - ERA Distributorseducation-era.com/lesson-plans/MATHOMAT_Senior_Booklet.pdf · 2015. 5. 24. · Mathomat Senior contains three sine/cosine curves. Each one can be used to

2

MATHOMAT

FEATURES OF MATHOMAT SENIOR

MATHOMAT

MATHOMAT SENIOR SPECIFICATIONSName Specifications

1 cosine/sine curve Period 4cm. Amplitude 1 cm

sine/cosine curve Period 8cm. Amplitude 1 cm

sine/cosine curve Period 4cm. Amplitude 2 cm

Circle 2.5 cm diameter

Circle 2 cm diameter

Cylinder Straight sides 2 cm, width 2 cm

Cone 2 cm base, 2.5 cm height

y = a (exponential graph)

Normal curve

Circle 1 cm diameter

Rectangle 3 cm x 2 cm

Parallelogram 3 cm, 2 cm, 30°

Ohombus 2 cm, 60°

Ellipse 4 cm x 2 cm

Equilateral triangle Inscribes within circle 29

Square 3 cm x 3 cm

Triangle (1, 1, 2 ) 3 cm, 3 cm, 45° , 45°, 90°

Sqaure pyramid

Ellipse 2 cm x 1 cm

Parallelogram 3 cm, 2 cm, 60°

y = tan x (tangent graph)

y = x (cubic graph)

Sqaure 2 cm x 1 cm

Sqaure 1.5 cm x 1.5 cm

Sqaure 1 cm x 1 cm

y = ½ x (quadratic graph)

y = x (quadratic graph)

4 cm x 1 cm

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

x

3

2

2

y = 2x (quadratic graph)

Ellipse3 cm diameterCircle4 cm diameterCircle

Triangle (1, 2, 3 )

2

OLM - Mathomat Senior Book redo _Layout 1 25/10/11 8:21 PM Page 4

Sine and cosine curves of various amplitudes and periods.

Accuraterulers.

Prism cluster.

Isometric drawing guides.

Quadratic graphs.

Trig graph scale.4 squares.5 circle sizes.

A complete list follows on the opposite page.

Unit circle and tangent line.

10 graphcurves.

Special triangles (1, 1, √2 and 1, 2, √3).

Three different ellipses.

Cylinder outline.

Pyramid outline.

11MATHOMAT

TANGENTOn a unit circle,

Tangent of an angle = position of the extended angle arm on the tangent line.A tangent line scale is marked on the right edge of Mathomat Senior, and must be re-drawn as shown before

the tangent of an angle can be read.

1.61.51.41.31.21.11.0

1.61.51.41.3

1.21.1

1.0

The diagram above shows that tangent of 50° = 1.2 (approx.) , or tan 30° = 1.2 (approx.).

tan 50° = 1.2 (approx.)

MATHOMAT

TRIGONOMETRIC SYMMETRY

SPECIAL TRIANGLES

Symmetry properties of the trigonometric function my be determined easily using Mathomat Senior’s unitcircle, which has angles in terms of marked.

The diagram below shows that

These statements may be generalised to find expressions for

Similar expressions may be derived for the tangent function(These tasks are left to the reader)

Shapes 17 and 32 are the ‘special triangles’ commonly used to determine trig values of key angles as shown below.

2H

T P

/2

3/2

Page 3: MATHOMAT - ERA Distributorseducation-era.com/lesson-plans/MATHOMAT_Senior_Booklet.pdf · 2015. 5. 24. · Mathomat Senior contains three sine/cosine curves. Each one can be used to

3

MATHOMAT

FEATURES OF MATHOMAT SENIOR

MATHOMAT

MATHOMAT SENIOR SPECIFICATIONSName Specifications

1 cosine/sine curve Period 4cm. Amplitude 1 cm

sine/cosine curve Period 8cm. Amplitude 1 cm

sine/cosine curve Period 4cm. Amplitude 2 cm

Circle 2.5 cm diameter

Circle 2 cm diameter

Cylinder Straight sides 2 cm, width 2 cm

Cone 2 cm base, 2.5 cm height

y = a (exponential graph)

Normal curve

Circle 1 cm diameter

Rectangle 3 cm x 2 cm

Parallelogram 3 cm, 2 cm, 30°

Ohombus 2 cm, 60°

Ellipse 4 cm x 2 cm

Equilateral triangle Inscribes within circle 29

Square 3 cm x 3 cm

Triangle (1, 1, 2 ) 3 cm, 3 cm, 45° , 45°, 90°

Sqaure pyramid

Ellipse 2 cm x 1 cm

Parallelogram 3 cm, 2 cm, 60°

y = tan x (tangent graph)

y = x (cubic graph)

Sqaure 2 cm x 1 cm

Sqaure 1.5 cm x 1.5 cm

Sqaure 1 cm x 1 cm

y = ½ x (quadratic graph)

y = x (quadratic graph)

4 cm x 1 cm

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

x

3

2

2

y = 2x (quadratic graph)

Ellipse3 cm diameterCircle4 cm diameterCircle

Triangle (1, 2, 3 )

2

OLM - Mathomat Senior Book redo _Layout 1 25/10/11 8:21 PM Page 4

10MATHOMAT

TANGENTOn a unit circle,

Tangent of an angle = position of the extended angle arm on the tangent line.A tangent line scale is marked on the right edge of Mathomat Senior, and must be re-drawn as shown before

the tangent of an angle can be read.

1.61.51.41.31.21.11.0

1.61.51.41.3

1.21.1

1.0

The diagram above shows that tangent of 50° = 1.2 (approx.) , or tan 30° = 1.2 (approx.).

tan 50° = 1.2 (approx.)

MATHOMAT

TRIGONOMETRIC SYMMETRY

SPECIAL TRIANGLES

Symmetry properties of the trigonometric function my be determined easily using Mathomat Senior’s unitcircle, which has angles in terms of marked.

The diagram below shows that

These statements may be generalised to find expressions for

Similar expressions may be derived for the tangent function(These tasks are left to the reader)

Shapes 17 and 32 are the ‘special triangles’ commonly used to determine trig values of key angles as shown below.

2H

T P

/2

3/2

Page 4: MATHOMAT - ERA Distributorseducation-era.com/lesson-plans/MATHOMAT_Senior_Booklet.pdf · 2015. 5. 24. · Mathomat Senior contains three sine/cosine curves. Each one can be used to

4

MATHOMAT

PERPENDICULAR LINES

PARALLEL LINES

Even previously tricky reflex angles maybe drawn and measured easily usingMathomat Senior’s circular protractor.

Use the lines that divide MathomatSenior vertically and horizontally asguides for constructing perpendicularlines, for example when drawing largerectangles.

Use the left edge ruler and straightedges of shapes 6 and 17 as shownto construct parallel lines 1 cm apart.

ANGLE MEASUREMENT AND CONSTRUCTION

MATHOMAT

ISOMETRIC LINES

Isometric Lines

These allow diagram like the one below to be drawn with relative ease.

OLM - Mathomat Senior Book redo _Layout 1 25/10/11 8:21 PM Page 6

9MATHOMAT

THREE DIMENSIONAL GEOMETRY

Use shapes 6, 19 Use shapes 7, 19 Use shapes 18

Use shapes 11, 12, 13 Use shapes 12, 19 Use shapes 23

Use shapes 5, 19 Use shapes 29, 31

Use shapes 15, 29

Use shapes 14, 31

Three dimensional solids maybe be sketched quickly and accurately using the shapes listed below.

OLM - Mathomat Senior Book redo _Layout 1 25/10/11 8:21 PM Page 9

MATHOMAT

LARGE SCALE POLYGONS

UNIT CIRCLE TRIGONOMETRYDefinitions od sine, cosine and tangent are easily explained and visualised using the circular protractor

which doubles as a ‘ unit circle’.

On a unit circle,

Sine of an angle = y co-ordinate Cosine of an angle = x co-ordinate

For example, the following diagram shows that

Sine of 30° = 0.5 and Cosine of 30° = 0.87 (approx.)

or, using mathematical shorthand,

sin 30° = 0.5 and cos 30° = 0.87 (approx.)

Sine and Cosine

Large polygons may be drawn using the letter guides around the outside of the circular protractor. Simply mark each

corner using the appropriate letter, and connect them.

The following letters are used around the circular protractor.

T - triangle, P - pentagon, H - hexagon, and O - octagon.

For a square, use the 0°, 90°, 180° and 270° holes on the edge of the circular protractor.

OLM - Mathomat Senior Book redo _Layout 1 25/10/11 8:21 PM Page 10

Page 5: MATHOMAT - ERA Distributorseducation-era.com/lesson-plans/MATHOMAT_Senior_Booklet.pdf · 2015. 5. 24. · Mathomat Senior contains three sine/cosine curves. Each one can be used to

5

MATHOMAT

PERPENDICULAR LINES

PARALLEL LINES

Even previously tricky reflex angles maybe drawn and measured easily usingMathomat Senior’s circular protractor.

Use the lines that divide MathomatSenior vertically and horizontally asguides for constructing perpendicularlines, for example when drawing largerectangles.

Use the left edge ruler and straightedges of shapes 6 and 17 as shownto construct parallel lines 1 cm apart.

ANGLE MEASUREMENT AND CONSTRUCTION

MATHOMAT

ISOMETRIC LINES

Isometric Lines

These allow diagram like the one below to be drawn with relative ease.

OLM - Mathomat Senior Book redo _Layout 1 25/10/11 8:21 PM Page 6

8MATHOMAT

THREE DIMENSIONAL GEOMETRY

Use shapes 6, 19 Use shapes 7, 19 Use shapes 18

Use shapes 11, 12, 13 Use shapes 12, 19 Use shapes 23

Use shapes 5, 19 Use shapes 29, 31

Use shapes 15, 29

Use shapes 14, 31

Three dimensional solids maybe be sketched quickly and accurately using the shapes listed below.

OLM - Mathomat Senior Book redo _Layout 1 25/10/11 8:21 PM Page 9

MATHOMAT

LARGE SCALE POLYGONS

UNIT CIRCLE TRIGONOMETRYDefinitions od sine, cosine and tangent are easily explained and visualised using the circular protractor

which doubles as a ‘ unit circle’.

On a unit circle,

Sine of an angle = y co-ordinate Cosine of an angle = x co-ordinate

For example, the following diagram shows that

Sine of 30° = 0.5 and Cosine of 30° = 0.87 (approx.)

or, using mathematical shorthand,

sin 30° = 0.5 and cos 30° = 0.87 (approx.)

Sine and Cosine

Large polygons may be drawn using the letter guides around the outside of the circular protractor. Simply mark each

corner using the appropriate letter, and connect them.

The following letters are used around the circular protractor.

T - triangle, P - pentagon, H - hexagon, and O - octagon.

For a square, use the 0°, 90°, 180° and 270° holes on the edge of the circular protractor.

OLM - Mathomat Senior Book redo _Layout 1 25/10/11 8:21 PM Page 10

Page 6: MATHOMAT - ERA Distributorseducation-era.com/lesson-plans/MATHOMAT_Senior_Booklet.pdf · 2015. 5. 24. · Mathomat Senior contains three sine/cosine curves. Each one can be used to

6MATHOMAT

GRAPHS OF TRIGONOMETRIC FUNCTIONSMathomat Senior contains three sine/cosine curves. Each one can be used to sketch any sine or cosine

graph by labeling the amplitude and period appropriately. For example, the following four graphs show four different functions,

but were all drawn using shape1.

Of course shapes2 and 3 may also be used to highlight different periods or amplitudes. Again, thechoice of axis can ‘force; a curve to match a particular equation.

MATHOMAT

TANGENT GRAPHS

GRAPHS OF OTHER FUNCTIONS

Shape 21 may maybe used to sketch tangent graphs. Again, an appropriate scale needs to be chosento ensure the curve matches the specified equation.

Mathomat Senior contains graphing curves for most of the major functions met in senior Maths classes.Curves and the shapes used to sketch then appear below.

7MATHOMAT

GRAPHS OF TRIGONOMETRIC FUNCTIONSMathomat Senior contains three sine/cosine curves. Each one can be used to sketch any sine or cosine

graph by labeling the amplitude and period appropriately. For example, the following four graphs show four different functions,

but were all drawn using shape1.

Of course shapes2 and 3 may also be used to highlight different periods or amplitudes. Again, thechoice of axis can ‘force; a curve to match a particular equation.

MATHOMAT

TANGENT GRAPHS

GRAPHS OF OTHER FUNCTIONS

Shape 21 may maybe used to sketch tangent graphs. Again, an appropriate scale needs to be chosento ensure the curve matches the specified equation.

Mathomat Senior contains graphing curves for most of the major functions met in senior Maths classes.Curves and the shapes used to sketch then appear below.

Page 7: MATHOMAT - ERA Distributorseducation-era.com/lesson-plans/MATHOMAT_Senior_Booklet.pdf · 2015. 5. 24. · Mathomat Senior contains three sine/cosine curves. Each one can be used to

6MATHOMAT

GRAPHS OF TRIGONOMETRIC FUNCTIONSMathomat Senior contains three sine/cosine curves. Each one can be used to sketch any sine or cosine

graph by labeling the amplitude and period appropriately. For example, the following four graphs show four different functions,

but were all drawn using shape1.

Of course shapes2 and 3 may also be used to highlight different periods or amplitudes. Again, thechoice of axis can ‘force; a curve to match a particular equation.

MATHOMAT

TANGENT GRAPHS

GRAPHS OF OTHER FUNCTIONS

Shape 21 may maybe used to sketch tangent graphs. Again, an appropriate scale needs to be chosento ensure the curve matches the specified equation.

Mathomat Senior contains graphing curves for most of the major functions met in senior Maths classes.Curves and the shapes used to sketch then appear below.

7MATHOMAT

GRAPHS OF TRIGONOMETRIC FUNCTIONSMathomat Senior contains three sine/cosine curves. Each one can be used to sketch any sine or cosine

graph by labeling the amplitude and period appropriately. For example, the following four graphs show four different functions,

but were all drawn using shape1.

Of course shapes2 and 3 may also be used to highlight different periods or amplitudes. Again, thechoice of axis can ‘force; a curve to match a particular equation.

MATHOMAT

TANGENT GRAPHS

GRAPHS OF OTHER FUNCTIONS

Shape 21 may maybe used to sketch tangent graphs. Again, an appropriate scale needs to be chosento ensure the curve matches the specified equation.

Mathomat Senior contains graphing curves for most of the major functions met in senior Maths classes.Curves and the shapes used to sketch then appear below.

Page 8: MATHOMAT - ERA Distributorseducation-era.com/lesson-plans/MATHOMAT_Senior_Booklet.pdf · 2015. 5. 24. · Mathomat Senior contains three sine/cosine curves. Each one can be used to

5

MATHOMAT

PERPENDICULAR LINES

PARALLEL LINES

Even previously tricky reflex angles maybe drawn and measured easily usingMathomat Senior’s circular protractor.

Use the lines that divide MathomatSenior vertically and horizontally asguides for constructing perpendicularlines, for example when drawing largerectangles.

Use the left edge ruler and straightedges of shapes 6 and 17 as shownto construct parallel lines 1 cm apart.

ANGLE MEASUREMENT AND CONSTRUCTION

MATHOMAT

ISOMETRIC LINES

Isometric Lines

These allow diagram like the one below to be drawn with relative ease.

OLM - Mathomat Senior Book redo _Layout 1 25/10/11 8:21 PM Page 6

8MATHOMAT

THREE DIMENSIONAL GEOMETRY

Use shapes 6, 19 Use shapes 7, 19 Use shapes 18

Use shapes 11, 12, 13 Use shapes 12, 19 Use shapes 23

Use shapes 5, 19 Use shapes 29, 31

Use shapes 15, 29

Use shapes 14, 31

Three dimensional solids maybe be sketched quickly and accurately using the shapes listed below.

OLM - Mathomat Senior Book redo _Layout 1 25/10/11 8:21 PM Page 9

MATHOMAT

LARGE SCALE POLYGONS

UNIT CIRCLE TRIGONOMETRYDefinitions od sine, cosine and tangent are easily explained and visualised using the circular protractor

which doubles as a ‘ unit circle’.

On a unit circle,

Sine of an angle = y co-ordinate Cosine of an angle = x co-ordinate

For example, the following diagram shows that

Sine of 30° = 0.5 and Cosine of 30° = 0.87 (approx.)

or, using mathematical shorthand,

sin 30° = 0.5 and cos 30° = 0.87 (approx.)

Sine and Cosine

Large polygons may be drawn using the letter guides around the outside of the circular protractor. Simply mark each

corner using the appropriate letter, and connect them.

The following letters are used around the circular protractor.

T - triangle, P - pentagon, H - hexagon, and O - octagon.

For a square, use the 0°, 90°, 180° and 270° holes on the edge of the circular protractor.

OLM - Mathomat Senior Book redo _Layout 1 25/10/11 8:21 PM Page 10

Page 9: MATHOMAT - ERA Distributorseducation-era.com/lesson-plans/MATHOMAT_Senior_Booklet.pdf · 2015. 5. 24. · Mathomat Senior contains three sine/cosine curves. Each one can be used to

4

MATHOMAT

PERPENDICULAR LINES

PARALLEL LINES

Even previously tricky reflex angles maybe drawn and measured easily usingMathomat Senior’s circular protractor.

Use the lines that divide MathomatSenior vertically and horizontally asguides for constructing perpendicularlines, for example when drawing largerectangles.

Use the left edge ruler and straightedges of shapes 6 and 17 as shownto construct parallel lines 1 cm apart.

ANGLE MEASUREMENT AND CONSTRUCTION

MATHOMAT

ISOMETRIC LINES

Isometric Lines

These allow diagram like the one below to be drawn with relative ease.

OLM - Mathomat Senior Book redo _Layout 1 25/10/11 8:21 PM Page 6

9MATHOMAT

THREE DIMENSIONAL GEOMETRY

Use shapes 6, 19 Use shapes 7, 19 Use shapes 18

Use shapes 11, 12, 13 Use shapes 12, 19 Use shapes 23

Use shapes 5, 19 Use shapes 29, 31

Use shapes 15, 29

Use shapes 14, 31

Three dimensional solids maybe be sketched quickly and accurately using the shapes listed below.

OLM - Mathomat Senior Book redo _Layout 1 25/10/11 8:21 PM Page 9

MATHOMAT

LARGE SCALE POLYGONS

UNIT CIRCLE TRIGONOMETRYDefinitions od sine, cosine and tangent are easily explained and visualised using the circular protractor

which doubles as a ‘ unit circle’.

On a unit circle,

Sine of an angle = y co-ordinate Cosine of an angle = x co-ordinate

For example, the following diagram shows that

Sine of 30° = 0.5 and Cosine of 30° = 0.87 (approx.)

or, using mathematical shorthand,

sin 30° = 0.5 and cos 30° = 0.87 (approx.)

Sine and Cosine

Large polygons may be drawn using the letter guides around the outside of the circular protractor. Simply mark each

corner using the appropriate letter, and connect them.

The following letters are used around the circular protractor.

T - triangle, P - pentagon, H - hexagon, and O - octagon.

For a square, use the 0°, 90°, 180° and 270° holes on the edge of the circular protractor.

OLM - Mathomat Senior Book redo _Layout 1 25/10/11 8:21 PM Page 10

Page 10: MATHOMAT - ERA Distributorseducation-era.com/lesson-plans/MATHOMAT_Senior_Booklet.pdf · 2015. 5. 24. · Mathomat Senior contains three sine/cosine curves. Each one can be used to

3

MATHOMAT

FEATURES OF MATHOMAT SENIOR

MATHOMAT

MATHOMAT SENIOR SPECIFICATIONSName Specifications

1 cosine/sine curve Period 4cm. Amplitude 1 cm

sine/cosine curve Period 8cm. Amplitude 1 cm

sine/cosine curve Period 4cm. Amplitude 2 cm

Circle 2.5 cm diameter

Circle 2 cm diameter

Cylinder Straight sides 2 cm, width 2 cm

Cone 2 cm base, 2.5 cm height

y = a (exponential graph)

Normal curve

Circle 1 cm diameter

Rectangle 3 cm x 2 cm

Parallelogram 3 cm, 2 cm, 30°

Ohombus 2 cm, 60°

Ellipse 4 cm x 2 cm

Equilateral triangle Inscribes within circle 29

Square 3 cm x 3 cm

Triangle (1, 1, 2 ) 3 cm, 3 cm, 45° , 45°, 90°

Sqaure pyramid

Ellipse 2 cm x 1 cm

Parallelogram 3 cm, 2 cm, 60°

y = tan x (tangent graph)

y = x (cubic graph)

Sqaure 2 cm x 1 cm

Sqaure 1.5 cm x 1.5 cm

Sqaure 1 cm x 1 cm

y = ½ x (quadratic graph)

y = x (quadratic graph)

4 cm x 1 cm

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

x

3

2

2

y = 2x (quadratic graph)

Ellipse3 cm diameterCircle4 cm diameterCircle

Triangle (1, 2, 3 )

2

OLM - Mathomat Senior Book redo _Layout 1 25/10/11 8:21 PM Page 4

10MATHOMAT

TANGENTOn a unit circle,

Tangent of an angle = position of the extended angle arm on the tangent line.A tangent line scale is marked on the right edge of Mathomat Senior, and must be re-drawn as shown before

the tangent of an angle can be read.

1.61.51.41.31.21.11.0

1.61.51.41.3

1.21.1

1.0

The diagram above shows that tangent of 50° = 1.2 (approx.) , or tan 30° = 1.2 (approx.).

tan 50° = 1.2 (approx.)

MATHOMAT

TRIGONOMETRIC SYMMETRY

SPECIAL TRIANGLES

Symmetry properties of the trigonometric function my be determined easily using Mathomat Senior’s unitcircle, which has angles in terms of marked.

The diagram below shows that

These statements may be generalised to find expressions for

Similar expressions may be derived for the tangent function(These tasks are left to the reader)

Shapes 17 and 32 are the ‘special triangles’ commonly used to determine trig values of key angles as shown below.

2H

T P

/2

3/2

Page 11: MATHOMAT - ERA Distributorseducation-era.com/lesson-plans/MATHOMAT_Senior_Booklet.pdf · 2015. 5. 24. · Mathomat Senior contains three sine/cosine curves. Each one can be used to

2

MATHOMAT

FEATURES OF MATHOMAT SENIOR

MATHOMAT

MATHOMAT SENIOR SPECIFICATIONSName Specifications

1 cosine/sine curve Period 4cm. Amplitude 1 cm

sine/cosine curve Period 8cm. Amplitude 1 cm

sine/cosine curve Period 4cm. Amplitude 2 cm

Circle 2.5 cm diameter

Circle 2 cm diameter

Cylinder Straight sides 2 cm, width 2 cm

Cone 2 cm base, 2.5 cm height

y = a (exponential graph)

Normal curve

Circle 1 cm diameter

Rectangle 3 cm x 2 cm

Parallelogram 3 cm, 2 cm, 30°

Ohombus 2 cm, 60°

Ellipse 4 cm x 2 cm

Equilateral triangle Inscribes within circle 29

Square 3 cm x 3 cm

Triangle (1, 1, 2 ) 3 cm, 3 cm, 45° , 45°, 90°

Sqaure pyramid

Ellipse 2 cm x 1 cm

Parallelogram 3 cm, 2 cm, 60°

y = tan x (tangent graph)

y = x (cubic graph)

Sqaure 2 cm x 1 cm

Sqaure 1.5 cm x 1.5 cm

Sqaure 1 cm x 1 cm

y = ½ x (quadratic graph)

y = x (quadratic graph)

4 cm x 1 cm

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

x

3

2

2

y = 2x (quadratic graph)

Ellipse3 cm diameterCircle4 cm diameterCircle

Triangle (1, 2, 3 )

2

OLM - Mathomat Senior Book redo _Layout 1 25/10/11 8:21 PM Page 4

Sine and cosine curves of various amplitudes and periods.

Accuraterulers.

Prism cluster.

Isometric drawing guides.

Quadratic graphs.

Trig graph scale.4 squares.5 circle sizes.

A complete list follows on the opposite page.

Unit circle and tangent line.

10 graphcurves.

Special triangles (1, 1, √2 and 1, 2, √3).

Three different ellipses.

Cylinder outline.

Pyramid outline.

11MATHOMAT

TANGENTOn a unit circle,

Tangent of an angle = position of the extended angle arm on the tangent line.A tangent line scale is marked on the right edge of Mathomat Senior, and must be re-drawn as shown before

the tangent of an angle can be read.

1.61.51.41.31.21.11.0

1.61.51.41.3

1.21.1

1.0

The diagram above shows that tangent of 50° = 1.2 (approx.) , or tan 30° = 1.2 (approx.).

tan 50° = 1.2 (approx.)

MATHOMAT

TRIGONOMETRIC SYMMETRY

SPECIAL TRIANGLES

Symmetry properties of the trigonometric function my be determined easily using Mathomat Senior’s unitcircle, which has angles in terms of marked.

The diagram below shows that

These statements may be generalised to find expressions for

Similar expressions may be derived for the tangent function(These tasks are left to the reader)

Shapes 17 and 32 are the ‘special triangles’ commonly used to determine trig values of key angles as shown below.

2H

T P

/2

3/2

Page 12: MATHOMAT - ERA Distributorseducation-era.com/lesson-plans/MATHOMAT_Senior_Booklet.pdf · 2015. 5. 24. · Mathomat Senior contains three sine/cosine curves. Each one can be used to

PO Box 6, Sandown Village, Vic, 3171, AustraliaTelephone: (03) 9796 1177 - Fax: (03) 9796 1832

www.mathomat.com.au

Published by Objective Learning Materials, a business of W&G Education Pty. Ltd. A.C.N. 051 847 637

1

Mathomat Senior has been specifically developed for Sketching andpresentation of work by students from years 10 to 12. Features such as aunit circle and tangent line for trigonometry study, graphing curves and3D soild sketch outline make Mathomat Senior an invaluable aid forprojects and classwork, particularly for topis such as Trigonometry,Geometry & Measurement and Fractions & Graphs.

A technical and creative drawing tool for senior secondary school students.

TEMPLATEMATHOMAT SENIOR

®