Inverse Trigonometric Functions Concepts

Professor Dave explains inverse trigonometric functions, focusing on inverse sine, cosine, and tangent. He discusses their domains, ranges, and how to evaluate them using the unit circle and calculators. The video emphasizes the importance of the horizontal line test for determining the existence of inverse functions and provides examples for better understanding.

What is the first step in finding the inverse of a function?

• Add the inverse function to both sides

• Divide both sides by the original function

• Multiply both sides by the inverse function

• Swap the variables and solve for the original variable

What is the inverse sine of root two over two?

• Three quarters pi

• Half pi

• Pi

• Quarter pi

What is the domain of the inverse sine function?

• Negative infinity to infinity

• Negative pi to pi

• Negative one to one

• Zero to pi

What is the range of the inverse sine function?

• Zero to pi

• Negative one to one

• Negative pi to zero

• Negative half pi to half pi

What is the inverse sine function also known as?

• Arccos

• Arctan

• Arcsin

• Arcsec

What is the angle that gives a sine of root two over two?

• Quarter pi

• Pi

• Three quarters pi

• Half pi

What is the range of the inverse sine function?

• Zero to pi

• Negative one to one

• Negative half pi to half pi

• Negative pi to zero

What is the inverse cosine of negative one half?

• Quarter pi

• Two thirds pi

• Half pi

• Three quarters pi

What is the domain of the inverse cosine function?

• Negative infinity to infinity

• Negative pi to pi

• Zero to pi

• Negative one to one

What is the range of the inverse cosine function?

• Negative one to one

• Negative half pi to half pi

• Negative pi to zero

• Zero to pi