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# Activity: The Big Bang Theory - exact values

## Purpose

To investigate trigonometric graphs and exact values.

## Achievement objectives

• M 8–6 Manipulate trigonometric expressions
• M 8–7 Form and use trigonometric, polynomial, and other non-linear equations

## Indicators

• Solves contextual problems by forming and solving equations.
• Analyses the existence of solutions in the context of the situation.
• Makes links to graphs of functions M8–2, curve fitting M8–4, solving equations M8–7, gradient functions M8–11, and manipulating expressions M7–6 and M8–6.

## Specific learning outcomes

Students will be able to:

• find and use exact values for trigonometric functions.

## Diagnostic snapshot(s)

Investigate trigonometric graphs using the following websites:

## Planned learning experiences

Show the first 6 minutes of ‘The Big Bang Theory’, Season 1, Episode 2.

(This link is to a YouTube clip. As the link may not be maintained, it may be more appropriate to buy or rent the DVD to show the class.)

In the clip, Sheldon says the value of sin30° is ½. How does Sheldon know this exact value?

What do you know that could confirm this value? How could you check this value out?

What other exact values might Sheldon know? How are these values linked to each other?

How are these exact values linked to graphs of the sin, tan and cos functions?

These websites can be used to check answers:

• Students could investigate the periodicity of exact values.
• How can you predict exact values? What families of angles have the same exact values?

• Physics

### Extension/enrichment ideas

• Apply these findings to practical applications such as tide times.
• Apply these findings to transformed trigonometric graphs.

## Planned assessment

This teaching and learning activity could lead towards assessment in the following achievement standard:

## Spotlight on

### Pedagogy

• Creating a supportive learning environment
• listening to all student responses
• valuing student contributions
• accepting all student responses as part of the learning process.

### Key competencies

• Thinking
• Students select appropriate methods and strategies when solving problems.
• Students make deductions, they justify and verify, interpret and synthesise and they create models.
• Students hypothesise, investigate, analyse and evaluate.
• Using language, symbols and texts
• Students interpret word problems and visual representations.
• Relating to others
• Students listen to others, they accept and value different viewpoints.
• Students work in groups, they debate solutions, negotiate meaning and communicate thinking.
• Managing self
• Students are prepared to take risks, make decisions, and persevere.
• Participating and contributing
• Students contribute to a culture of inquiry and learning. They share strategies and thinking and they empower and enable others.