Question

NEED HELP PLEASE

1.) The function Tan θ = y has θ restricted to
2.) Find θ when Cos-1 0 = θ. Give your answer in degrees
3.) The domain of function Tan-1 a = θ is restricted to

Answer 1

Tan 90 is undefined (for example)

Answer 2

so would it be {θ | -90º ≤θ ≤90º}?

Answer 3

Well, it's undefined `at` -90 and 90.
So we need a strict inequality, can't have the `or equal to`.

But yes, that gives us one interval of tangent.
There are a few more +_+ infinitely many more.
Umm lemme think of how we would write this..

Answer 4

ohh i see

Answer 5

So you're trying to write it in set notation?
This is kinda sloppy.... but I dunno maybe it will help.
\[\Large\rm \{\theta|-\infty\lt\theta\lt\infty,\qquad\theta\ne \frac{\pi}{2}+k\pi,\qquad k\in\mathbb Z\}\]

Answer 6

So I'm saying that theta can take on EVERY value, except pi/2 and any angle that's pi/2 plus/minus a multiple of pi.

Answer 7

So if k=-1.
It gives us theta `cannot equal` -pi/2, yes?

Answer 8

Oh you were doing this in degrees!
Doh! I probably made this more difficult for you :c

Answer 9

yeah haha it says to do it in degrees that's why i was processing what you were trying to say because I have not done it like that before

Answer 10

\[\Large\rm \{\theta|-\infty\lt\theta\lt\infty,\qquad\theta\ne 90^{\circ}+k\cdot180^{\circ},\qquad k\in\mathbb Z\}\]Maybe it's still a little confusing :)
But here's what it looks like in degrees.