Chapter 4, Problem 98RE

To determine

Whether the given statement is true or false.

Answer to Problem 98RE

The given statement is false.

Explanation of Solution

Given:

The given statement is:

  $\arctan \left(-1\right)=\frac{3\pi }{4}\text{because tan}\left(\frac{3\pi }{4}\right)=-1$

In accordance with the definition of the inverse trigonometric tangent function:

  $\begin{array}{c}y=\arctan \left(x\right)\\ \tan y=x\end{array}$

Now taking $\arctan \left(-1\right)$ , the angle can be represented by $\left(\frac{2n+1}{4}\right)\pi$ .

Hence, by putting the value of the n , the angle can be anything.

Hence, when the domain of the angles are not given, then the one angle cannot be the answer to the given problem.

Therefore, the given statement is false.