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.
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?