The principal value of tan inverse 4 is π over 4.

The statement about the principal value of tan inverse 4 being π over 4 is incorrect. The correct principal value of tan inverse 4, often written as arctan(4), is actually a different angle.

Understanding Arctangent Values

The function tan inverse, or arctan, gives the angle whose tangent is a specific value. For example:

• tan(π/4) = 1
• tan(π/2) is undefined

Calculating Arctan(4)

To find the angle whose tangent is 4, we can use a calculator or reference tables. The value of arctan(4) is approximately:

1.3258 radians or about 75.96 degrees.

Key Takeaways

In summary, the principal value of tan inverse 4 is not π over 4, but rather around 1.3258 radians. This angle corresponds to a tangent value of 4, which is much steeper than the angle for π over 4.