Why we avoid the law of sines over the law of cosines with ambiguous triangles

The video tutorial covers the concepts of sine and cosine inverse functions, focusing on their domain restrictions and how these affect angle calculations. It explains the relationships between angles, reflections, and cofunction identities. The tutorial also discusses the implications of these restrictions when dealing with triangles, particularly in the context of the law of sines and cosines, highlighting the challenges in determining obtuse angles.

What is the sine inverse of 1/2 and why is it restricted to 30 degrees?

Explain the restrictions on the sine inverse function and how they affect the possible answers.

How does the cosine inverse function differ in its restrictions compared to the sine inverse function?

What is the significance of the angles 60 degrees and 120 degrees in relation to cosine of 1/2?

Discuss the relationship between sine and cosine functions as cofunctions.

Why can't a triangle have an angle larger than 180 degrees, and how does this relate to the use of inverse functions?

What challenges arise when using sine inverse to find angles in triangles, particularly regarding acute and obtuse angles?