Here are three triangles with some side lengths and angles marked. Express the missing side lengths in terms of \(\sin \theta\), \(\cos \theta\) and \(\tan \theta.\)
How can using side length ratios for \(\sin \theta\), \(\cos \theta\) and \(\tan \theta\) help you?
These triangles are all similar. How can you use this to help you?
What do you notice if you compare the results of the two approaches?
We now have six trigonometric functions. From the side lengths in the triangles above, what relationships can you find between these functions?