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Mathematics / Year 10 / Measurement and Geometry / Pythagoras and trigonometry

View on Australian Curriculum website Australian Curriculum, Assessment and Reporting Authority
Curriculum content descriptions

Use the unit circle to define trigonometric functions, and graph them with and without the use of digital technologies (ACMMG274)

Elaborations
  • establishing the symmetrical properties of trigonometric functions
  • investigating angles of any magnitude
  • understanding that trigonometric functions are periodic and that this can be used to describe motion
General capabilities
  • Numeracy Numeracy
  • Critical and creative thinking Critical and creative thinking
  • ICT capability Information and Communication Technology (ICT) capability
ScOT terms

Unit circles,  Periodic functions

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Year level 9-10
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Learning area Mathematics
Interactive resource

Trigonometry: cosine

Look at an explanation of the trigonometric ratios: sine, cosine and tangent. Adjust the angles of a right angle triangle within a unit circle (radius of one unit). Identify the cosine ratio and enter the cosine values of angles from 0–90 degrees into a table. Answer questions about the cosine values. This learning object ...

Interactive resource

Trigonometry: sine

Look at an explanation of the trigonometric ratios: sine, cosine and tangent. Adjust the angles of a right-angled triangle within a unit circle (radius of one unit). Find corresponding sides in similar triangles and find relationships between ratios. Identify the sine ratio and enter the sine values of angles from 0–90 ...

Interactive resource

Trigonometry: tangent

Look at an explanation of the trigonometric ratios: sine, cosine and tangent. Adjust the angles of a right-angled triangle within a unit circle (radius of one unit). Identify the tangent ratio and enter the tangent values of angles from 0–90 degrees into a table. Answer questions about the tangent values. This learning ...

Assessment resource

Trigonometry: assessment

Test your understanding of angles and their sine, cosine and tangent values. Use a unit circle tool to find sine, cosine and tangent values in different quadrants. Use the tool to find the angle when given sine, cosine or tangent values. Determine the values for angles between 0° and 360°. Solve problems by using the unit ...

Interactive resource

Trig degrees: sine tool

Use a unit circle tool to explore sine values for angles between 0° and 360°. Observe the graph being drawn as each sine value is plotted. This learning object is one in a series of nine objects. Three objects in the series are also packaged as a combined learning object.

Interactive resource

Trig degrees: cosine tool

Use a unit circle tool to explore cosine values for angles between 0° and 360°. Observe the graph being drawn as each cosine value is plotted. This learning object is one in a series of nine objects. Three objects in the series are also packaged as a combined learning object.

Interactive resource

Trig degrees: cosine to 360: demo

Watch a demonstration showing how cosine is defined in the unit circle. Connect this definition with the right-angled triangle definition commonly used in right-angled triangle trigonometry. This learning object is one in a series of nine objects. Three objects in the series are also packaged as a combined learning object.

Interactive resource

Trig degrees: sine to 360

Use a unit circle tool to explore sine values in different quadrants. Determine the sin Ø values for angles between 0° and 360°. Observe the symmetry and patterns of the functions to predict the behaviour of sin Ø in different quadrants. Observe the graph animate and visually connect it with the unit circle tool and table ...

Teacher resource

Trigonometric functions and circular measure

This is a teacher resource for trigonometric functions and circular measure consisting of a website, a PDF with identical content and a number of screencasts discussing the solutions of exercises. It contains an introduction to the trigonometric functions and their uses. The functions are introduced and their properties ...

Interactive resource

Trig degrees: sine to 360: demo

Watch a demonstration showing how sine is defined in the unit circle. Connect this definition with the right-angled triangle definition commonly used in right-angled triangle trigonometry. This learning object is one in a series of nine objects. Three objects in the series are also packaged as a combined learning object.

Interactive resource

Trig degrees: tangent tool

Use a unit circle tool to explore tangent values for angles between 0° and 360°. Use the information to determine what the graph of tan Ø will look like. This learning object is one in a series of nine objects. Three objects in the series are also packaged as a combined learning object.

Interactive resource

Trig degrees: tangent to 360: demo

Watch a demonstration showing how tangent is defined in the unit circle. Connect this definition with the right-angled triangle definition commonly used in right-angled triangle trigonometry. This learning object is one in a series of nine objects. Three objects in the series are also packaged as a combined learning object.

Interactive resource

Trig degrees: cosine to 360

Use a unit circle tool to explore cosine values in different quadrants. Determine the cos Ø values for angles between 0° and 360°. Observe the symmetry and patterns of the functions to predict the behaviour of cos Ø in different quadrants. Observe the graph animate and visually connect it with the unit circle tool and table ...

Interactive resource

Trig degrees: tangent to 360

Use a unit circle tool to explore tangent values in different quadrants. Determine the tan Ø values for angles between 0° and 360°. Observe the symmetry and patterns of the functions to predict the behaviour of tan Ø in different quadrants. Observe the graph animate and visually connect it with the unit circle tool and ...

Teacher resource

Secondary mathematics: using real data

These seven learning activities, which focus on the use of 'real data' using a variety of tools (software) and devices (hardware), illustrate the ways in which content, pedagogy and technology can be successfully and effectively integrated in order to promote learning. In the activities, teachers use the three content strands ...

Moving Image

Applying trigonometry: leaning tower

The Leaning Tower of Gingin is the centrepiece of the Gravity Discovery Centre. The Catalyst team of Derek, Simon and Anja drop watermelons from the tower, to examine the rate at which they fall. They are testing Galileo's theory about falling objects. The dimensions of the tower provide an opportunity to apply some basic ...

Teacher resource

reSolve: Trigonometry: Rule of Twelfths

This sequence of three lessons gives students the opportunity to explore how tidal variations can be modelled and predicted using trigonometric functions and approximated with useful 'rules of thumb'. Students use real tidal data to explore how sailors make predictions at sea, draw their own graphs using a range of approximation ...