Question

TRIGONOMETRY What is the y-value for the function y=tan x if x= -11tt/4?

Answer 1

The value of the function is given below as

`y=\tan x,x=-(11\pi)/(4)`

Substituting the value of x, we will have

`\begin{gathered} y=\tan x \\ y=\tan (-(11)/(4)\pi) \end{gathered}`

By converting from radians to degrees, we will have

`\begin{gathered} y=\tan (-(11)/(4)\pi) \\ -(11)/(4)\pi=-(11)/(4)*180=-495 \end{gathered}`
`\begin{gathered} y=\tan (-(11)/(4)\pi)=\tan (-495) \\ \tan (-495)=\tan (-495+360)=\tan (-135) \end{gathered}`

Using the trigonometric identity below, we will have

`\begin{gathered} \tan (-\theta)=-\tan \theta \\ \tan (-135)=-\tan 135^0 \\ \text{Tan}135=-1 \\ \tan (-135)=-(-1) \\ \tan (-135)=1 \\ y=\tan (-(11)/(4)\pi)=1 \end{gathered}`

Hence,

The final answer = 1