Answer:
The value of the function is given below as
[tex]y=\tan x,x=-\frac{11\pi}{4}[/tex]
Substituting the value of x, we will have
[tex]\begin{gathered} y=\tan x \\ y=\tan (-\frac{11}{4}\pi) \end{gathered}[/tex]
By converting from radians to degrees, we will have
[tex]\begin{gathered} y=\tan (-\frac{11}{4}\pi) \\ -\frac{11}{4}\pi=-\frac{11}{4}\times180=-495 \end{gathered}[/tex][tex]\begin{gathered} y=\tan (-\frac{11}{4}\pi)=\tan (-495) \\ \tan (-495)=\tan (-495+360)=\tan (-135) \end{gathered}[/tex]
Using the trigonometric identity below, we will have
[tex]\begin{gathered} \tan (-\theta)=-\tan \theta \\ \tan (-135)=-\tan 135^0 \\ \text{Tan}135=-1 \\ \tan (-135)=-(-1) \\ \tan (-135)=1 \\ y=\tan (-\frac{11}{4}\pi)=1 \end{gathered}[/tex]
Hence,
The final answer = 1
