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Year 10 Interactive Maths - Second Edition


Projects

Project 15.1  Table of Sine Values

Draw the unit circle shown, and divide the radius into 10 equal parts so that each part represents 0.1.

3.  Use a ruler and protractor to create a table of sine values correct to one decimal place.

6.  If a plane is divided into four equal parts by a set of axes, then each part is called a quadrant.

In the first quadrant, the angle is between 0º and 90º.
In the second quadrant, the angle is between 90º and 180º.
In the third quadrant, the angle is between 180º and 270º.
In the fourth quadrant, the angle is between 270º and 360º.

We observe from the unit circle and question 3 that the value of sine of an angle in the first quadrant is + (i.e. positive). What is the sign (i.e. positive or negative) of the sine of an angle in the:
a.  second quadrant.
b.  third quadrant.
c.  fourth quadrant.

Your report should include the following:

  • A statement of the project in your own words
  • The tables, graphs and all working
  • References
  • Acknowledgments
  • Appendices


Project 15.2  Table of Cosine Values

Draw the unit circle shown, and divide the radius into 10 equal parts so that each part represents 0.1.

1.  Use a ruler and protractor to create a table of cosine values correct to one decimal place.

4.  If a plane is divided into four equal parts by a set of axes, then each part is called a quadrant.

In the first quadrant, the angle is between 0º and 90º.
In the second quadrant, the angle is between 90º and 180º.
In the third quadrant, the angle is between 180º and 270º.
In the fourth quadrant, the angle is between 270º and 360º.

We observe from the unit circle and question 1 that the value of cosine of an angle in the first quadrant is + (i.e. positive). What is the sign (i.e. positive or negative) of the cosine of an angle in the:
a.  second quadrant.
b.  third quadrant.
c.  fourth quadrant.

Your report should include the following:

  • The statement of the project in your own words
  • The tables, graphs and all working
  • References
  • Acknowledgments
  • Appendices


Project 15.3  Table of Tangent Values

Draw the unit circle shown, and divide the radius into 10 equal parts so that each part represents 0.1.

1. Use a ruler and protractor to create a table of tangent values correct to one decimal place.

4.  If a plane is divided into four equal parts by a set of axes, then each part is called a quadrant.

In the first quadrant, the angle is between 0º and 90º.
In the second quadrant, the angle is between 90º and 180º.
In the third quadrant, the angle is between 180º and 270º.
In the fourth quadrant, the angle is between 270º and 360º.

We observe from the unit circle and question 1 that the value of the tangent of an angle in the first quadrant is + (i.e. positive). What is the sign (i.e. positive or negative) of the tangent of an angle in the:
a.  second quadrant.
b.  third quadrant.
c.  fourth quadrant.

Your report should include the following:

  • The statement of the project in your own words
  • The tables, graphs and all working
  • References
  • Acknowledgments
  • Appendices

 

Project 15.4  Trigonometric Identities

Draw the unit circle shown, and divide the radius into 10 equal parts so that each part represents 0.1.


Project 15.5  Displacement and Time

Equipment required
  • A piece of string
  • Bob
  • Ruler
  • Graph paper

Periodic motion enables us to measure small intervals of time accurately.

Let t be the time measured from the rest position of the pendulum (as shown above) and d be the horizontal displacement to the right or left of the bob from the rest position.

Assume that the displacement, d, is positive when the bob is to the right of the rest position; otherwise, d is negative.

1.  Complete the following table. You may extend the table further.

2.  Plot d against t; and hence draw a curve of best fit.

3a.  Does the curve represent a graph of a periodic function?
  b.  Name the function; and state its rule.

4a.  What is the period of the sine curve?
  b.  What is the time for one oscillation (i.e. one complete swing forward and back)?
  c.  What is the relation between the time for one oscillation and the period of sine curve?
  d.  What is the relationship between the maximum displacement and the amplitude of the sine curve?


Project 15.6  Motion of the Hand of a Clock

Equipment required
  • Clock
  • Ruler
  • Graph paper

The minutes hand of a clock is pivoted at the centre of the face of a clock and the tip of the minutes hand completes one revolution in 60 minutes.

Let h cm be the height of the tip of the minutes hand above the horizontal at time t minutes where t is measured from the 12 o'clock position.

1.  Complete the following table:

3.  Use your algebraic model to find:
a.  h when t = 12 minutes
b.  t when h = 3 cm


Extension

The motion of the tip of the minutes hands may be related to the angle swept out in degrees.

5.  How much time is taken to sweep out an angle of 24o by the minutes hand?

6.  Complete the following table:


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