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 °, Cos 40 °
Sin 70 °, Cos 20 °
Sin 15°,Cos 75°

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.


why not install a flash player in your browser so you can use this interactiviy?




The film suggests a way to understand Sine and Cosine ratios (or lengths, if the hypotenuse has length one), for angles beyond the 0 ° to 90° range, in other words beyond angles which occur in right-angled triangles.

Which of these statements do you think are true?:

sin 150 ° = sin 30° (notice that 180 - 30 = 150)

sin 150 ° = sin 330 °

sin 150 ° = sin 210°

sin 30° = sin 330 °

cos 30 ° = cos 330 °

cos 50° = cos 130 °

sin 150 ° = cos 30 °

sin 150 ° = cos 60 °

sin 300 ° = cos 30 °

You could use your calculator to check.

What other relationships can you find?

Can you make some general statements?