Properties of the Inverse Tangent Function

The video tutorial explores the properties of the tan inverse function, focusing on the relationship between tan inverse of x and tan inverse of 1/x. It demonstrates that the sum of these functions equals pi/2, and discusses the odd nature of the tan inverse function. The tutorial also examines the behavior of the function for negative x values and analyzes the graph of y equals tan inverse, highlighting its odd function characteristics.

What is the result when you take the tan inverse of x and the tan inverse of 1/x?

• Zero

• Pi

• Pi/2 minus theta

• Theta

What property of the tan inverse function is highlighted when x is less than zero?

• It is even

• It is odd

• It is linear

• It is constant

How does the odd property of tan inverse affect the function when x is negative?

• It becomes negative

• It remains the same

• It becomes undefined

• It becomes positive

What happens to the graph of y = tan inverse x when x equals zero?

• It equals pi/2

• It equals pi

• It equals zero

• It is undefined

For positive x, what is the value of y = tan inverse x?

• Pi/2

• Undefined

• Negative pi/2

• Zero

For negative x, what is the value of y = tan inverse x?

• Undefined

• Pi/2

• Zero

• Negative pi/2

What happens to the function y = tan inverse x when x is positive?

• It is undefined

• It equals negative pi/2

• It equals pi/2

• It equals zero

What is the nature of the function y = tan inverse x + tan inverse (1/x)?

• Constant

• Linear

• Odd

• Even

What is the result of adding two odd functions?

• A constant function

• A linear function

• An even function

• Another odd function

What is the graphical representation of y = tan inverse x for all x?

• An odd function

• A straight line

• A parabola

• A circle