This is called the Unit Circle (0,1) (1,0) (-1,0) (0,-1)

𝐻𝑜𝑤 𝑙𝑜𝑛𝑔 𝑖𝑠 𝑡ℎ𝑒 𝑟𝑒𝑑 𝑙𝑒𝑛𝑔𝑡ℎ?

𝐻𝑜𝑤 𝑙𝑜𝑛𝑔 𝑖𝑠 𝑡ℎ𝑒 𝑟𝑒𝑑 𝑙𝑒𝑛𝑔𝑡ℎ?

𝐻𝑜𝑤 𝑙𝑜𝑛𝑔 𝑖𝑠 𝑡ℎ𝑒 𝑟𝑒𝑑 𝑙𝑒𝑛𝑔𝑡ℎ?

How long is the red length?

How long is the red length?

How long is the red length?

How long is the red length?

How long is the red length?

How long is the red length?

How long is the red length?

How long is the red length?

How long is the red length?

How long is the red length?

How long is the red length?

How long is the red length?

How long is the red length?

How long is the red length?

How long is the red length?

How long is the red length?

What is the name of the blue length?

What is the name of the blue length?

What is the name of the blue length?

What is the name of the blue length?

What is the name of the blue length?

What is the name of the blue length?

What is going to happen when the red line has turned 90 degrees?

What is going to happen when the red line has turned 90 degrees?

What is going to happen when the red line has turned 90 degrees?

What is going to happen when the red line has turned 90 degrees?

When else is this going to happen?

When else is this going to happen?

When else is this going to happen?

When else is this going to happen?

When else is this going to happen?

When else is this going to happen?

When else is this going to happen?

When else is this going to happen?

When else is this going to happen?

When else is this going to happen?

When else is this going to happen?

When else is this going to happen?

When else is this going to happen?

Tangent Sine (1,0) Cosine

tan θ 1 sin θ θ cos θ 1

What does the value 0.866… represent? 0.866.. does represent a length but be careful here as a length cannot become negative later on.. y represents the value of the y axis. What does the value 0.866… represent?

Work out y

𝑦=0.5

Work out y

𝑦= sin 45 = sin 135 =0.707…

Work out y

𝑦= − sin 20 = sin 200 =−0.342…

Work out y

𝑦= − sin 50 = sin 230 =−0.766…

Work out y

𝑦= − sin 20 = sin 340 =−0.342…

The Sine Graph - your turn θ 0° 30° 60° 90° 180° 210° 240° 270° 300° 330° 360° sin 𝜃 Which values do we know without using a calculator?

With your calculator complete the table and plot the coordinates. The Sine Graph θ 0° 30° 60° 90° 180° 210° 240° 270° 300° 330° 360° 𝐬𝐢𝐧 𝛉 0.5 3 2 Use Worksheet – do not allow students to join coordinates until they have seen the Geogebra demo next With your calculator complete the table and plot the coordinates.

Unit Circle Demo Show demo to allow students to access their Sine Graph

The Cosine Graph - your turn θ 0° 30° 60° 90° 180° 210° 240° 270° 300° 330° 360° 𝐜𝐨𝐬 𝛉 Which values do we know without using a calculator?

The Cosine Graph - your turn θ 0° 30° 60° 90° 180° 210° 240° 270° 300° 330° 360° 𝐜𝐨𝐬 𝛉 3 2 0.5 Use Worksheet as before Complete the table and plot the graph on your worksheet

The Tangent Graph - your turn θ 0° 30° 60° 90° 180° 210° 240° 270° 300° 330° 360° 𝐭𝐚𝐧 𝛉 Which values do we know without using a calculator?

The Tangent Graph - your turn θ 0° 30° 60° 90° 180° 210° 240° 270° 300° 330° 360° 𝐭𝐚𝐧 𝛉 3 3 3 Complete the table and plot the graph on your worksheet

A function which repeats after a fixed interval is called periodic What do you think is the period of the sine function?

What are the maximum and minimum values of the sine function?

In your book: What is the period of the Cosine function? 1. Look at your Cosine Graph: What is the period of the Cosine function? What are the maximum and minimum values of the Cosine function? 2. Look at your Tangent Graph: What is the period of the Tangent function? Why isn’t the Tangent graph one continuous curve? 3. Sketch the graph 𝑦= cos 𝑥 −90 for 0°≤𝑥≤360 on the spare axes provided. What do you notice? 4. Sketch the graph of 𝑦= sin 𝑥 cos 𝑥 for −90°≤𝑥≤90°