The video tutorial by Amal Kumar explores the concept of inverse trigonometric functions, focusing on the problem of finding the exact value of tan inverse tan of 4 PI by 3. The tutorial explains why the expected result of f inverse of f(x) equals x does not hold in this case. It delves into the calculation of the angle 4 PI by 3, its position in the Cartesian plane, and the properties of the tangent function in different quadrants. The solution involves understanding the acute angle and using trigonometric identities to find the correct value. The tutorial concludes by emphasizing the importance of understanding the domain of inverse functions and how it affects the results.

What is the main problem discussed in the video?

• Finding the exact value of tan inverse of tan 4π/3

• Finding the exact value of cos inverse of cos 4π/3

• Finding the exact value of sin inverse of sin 4π/3

• Finding the exact value of cot inverse of cot 4π/3

What is the angle 4π/3 equivalent to in the Cartesian plane?

• An angle in the fourth quadrant

• An angle in the second quadrant

• An angle in the first quadrant

• An angle in the third quadrant

In which quadrant is the angle 4π/3 located?

• Second quadrant

• First quadrant

• Third quadrant

• Fourth quadrant

What is the acute angle associated with 4π/3?

• π/6

• π/4

• π/3

• π/2

What is the value of tan π/3?

• 0

• 1/√3

• √3

• 1

What is the significance of the standard triangle in this context?

• It helps in calculating sin values

• It helps in calculating cos values

• It helps in calculating tan values

• It helps in calculating cot values

What is the acute angle used in the standard triangle for tan π/3?

• π/6

• π/4

• π/3

• π/2

What is the result of tan inverse of tan 4π/3?

• 2π/3

• π

• 4π/3

• π/3

What is the value of tan inverse of √3?

• π/3

• π/6

• π/4

• π/2

Why does tan inverse of tan X not always equal X?

• Because tan X is always negative

• Because the inverse function has a restricted domain

• Because the inverse function is not defined for all X

• Because tan is not defined for all X