GIVEN:
We are given the following trigonometric expression;
[tex]Tan^{-1}(-1)[/tex]
Required;
We are required to evaluate and answer both in radians and in degrees.
Step-by-step solution;
We shall begin by using the trig property;
[tex]tan^{-1}(-x)=-tan^{-1}(x)[/tex]
Therefore, we now have;
[tex]tan^{-1}(-1)=-tan^{-1}(1)[/tex]
We now use the table of common values and we'll have;
[tex]tan^{-1}(1)=\frac{\pi}{4}[/tex]
Therefore;
[tex]-tan^{-1}(1)=-\frac{\pi}{4}[/tex]
We can now convert this to degrees;
[tex]\begin{gathered} Convert\text{ }radians\text{ }to\text{ }degrees: \\ \frac{r}{\pi}=\frac{d}{180} \end{gathered}[/tex]
Substitute for r (radian measure):
[tex]\begin{gathered} \frac{-\frac{\pi}{4}}{\pi}=\frac{d}{180} \\ \\ -\frac{\pi}{4}\div\frac{\pi}{1}=\frac{d}{180} \\ \\ -\frac{\pi}{4}\times\frac{1}{\pi}=\frac{d}{180} \\ \\ -\frac{1}{4}=\frac{d}{180} \end{gathered}[/tex]
Now we can cross multiply;
[tex]\begin{gathered} -\frac{180}{4}=d \\ \\ -45=d \end{gathered}[/tex]
Therefore,
ANSWER:
[tex]\begin{gathered} radians=-\frac{\pi}{4} \\ \\ degrees=-45\degree \end{gathered}[/tex]
