Question

How do you find the exact value of tan270°?

Answer 1

`oo`

Explanation:

`2pi=360^o`
`pi=180^o`
`pi+pi/2=180^o+90^o=270^o`
`tan270^o=tan(pi+pi/2)=tan(pi/2)=oo`
as `tan`is positive in 3rd quadrant

Answer 2

`tan(270^@)` is undefined

Explanation:

`tan(theta) = y/x` for an angle `theta` in standard position on the Cartesian axis system.

For an angle of `theta = 270^@`
`color(white)("X")`as `theta rarr 270^@` `color(white)("XXX")xrarr0` (positively or negatively depending upon which quadrant `theta` approaches `270^@` from)

Since division by `0` is undefined
`color(white)("XXX")tan(270^@) = (y=-1)/(xrarr0)` is undefined.