This problem is a follow on to the problems Round and Round and Round and Where Is the Dot?

Use your calculator to find decimal values for the following:
$Sin 50^{\circ}$ , $Cos 40^{\circ}$
$Sin 70^{\circ}$ , $Cos 20^{\circ}$
$Sin 15^{\circ}$ , $Cos 75^{\circ}$

What do you notice and why does that happen?

Look at the film below - does that fit with your description?

Look especially at Stage 3 of the film, you may also find the Pause button useful.

The film suggests a way to understand Sine and Cosine ratios (or lengths, if the hypotenuse has length one), for angles beyond the

0^{\circ}

90^{\circ}

range, in other words beyond angles which occur in right-angled triangles.

Which of these statements do you think are true?:

$\sin 150^{\circ} = \sin 30^{\circ}$ (notice that 180 - 30 = 150)

$\sin 150^{\circ} = \sin 330^{\circ}$

$\sin 150^{\circ} = \sin 210^{\circ}$

$\sin 30^{\circ} = \sin 330^{\circ}$

$\cos 30^{\circ} = \cos 330^{\circ}$

$\cos 50^{\circ} = \cos 130^{\circ}$

$\sin 150^{\circ} = \cos 30^{\circ}$

$\sin 150^{\circ} = \cos 60^{\circ}$

$\sin 300^{\circ} = \cos 30^{\circ}$

You could use your calculator to check.

What other relationships can you find?

Can you make some general statements?