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 domain restriction for the sine inverse function?

• Angles in the 1st and 4th quadrants

• Angles in the 2nd and 3rd quadrants

• Angles between 0 and 90 degrees

• Angles between 0 and 180 degrees

Which quadrants are considered for the cosine inverse function?

• 1st and 4th quadrants

• 3rd and 4th quadrants

• 2nd and 3rd quadrants

• 1st and 2nd quadrants

How is the angle in the second quadrant related to the angle in the first quadrant for cosine?

• It is the negative of the angle in the first quadrant

• It is the same as the angle in the first quadrant

• It is double the angle in the first quadrant

• It is half the angle in the first quadrant

What is the relationship between sine and cosine known as?

• Quadrant identities

• Reflection identities

• Cofunction identities

• Inverse identities

Why can't sine inverse be used to find obtuse angles in triangles?

• It only provides angles between 0 and 90 degrees

• It only provides angles between 0 and 180 degrees

• It only provides angles in the 2nd quadrant

• It only provides angles in the 1st quadrant

Which law helps in identifying obtuse angles in triangles?

• Law of Sines

• Law of Cosines

• Law of Tangents

• Law of Quadrants

What is the main limitation of using sine inverse in triangle calculations?

• It cannot find acute angles

• It cannot find obtuse angles

• It cannot find right angles

• It cannot find angles larger than 180 degrees