Students will learn how to evaluate inverse trig functions using the unit circle. For example, evaluate \(\sin^{-1}(1/2).\)
Evaluating inverse trig functions using the unit circle
Concude by giving your students this challenge:
Find the radius of the circle:
Prereqs include knowing a rectangle has four right angles, knowing the intersecting chords theorem, and knowing the Pythagorean theorem. Here's the solution. Before watching this video, you should be aware it contains one mistake. He uses Thales's theorem to conclude AE is a diameter, but Thales's theorem can only be used to prove an angle is \(90^\circ,\) subject to certain conditions. In this case, we know AE is a diameter because ABE is a right angle. If it's not obvious, you could imagine copying the path ABE, rotating it 180 deg around the center of the circle. What you get is a rectangle circumscribed by the circle. Thus AE is the diagonal of the rectangle, and O must be its midpoint, as any rectangle and its circumcircle have the same center, by symmetry.