How do i find the domain and range for h(t) = cot t

Question

anonymous · Answer

are there any restrictions on t?

anonymous · Answer

The mineral dissolves in hot water, as the water coolsthe mineral compounds leave  and the minerals form

anonymous · Answer

i think i answered the wrong question. so sorry about that. you can take away the medal you gave to me. so sorry about that.

anonymous · Answer

there arent any restrictions

anonymous · Answer

Mhm, why do you say that

anonymous · Answer

you asked if there were restrictions on t and thats my answer

anonymous · Answer

what I mean is, is there a value of t that will give you a discontinuity (is there a hole or a verticle asymptote in the graph)?

anonymous · Answer

I've been in calc for 4 days i dont know what you mean forgive me

anonymous · Answer

do you know what the domain is of 

$$(x+1)(x-1)/(x-1)$$?

anonymous · Answer

no

anonymous · Answer

the refers to the valid range of inputs (in the above case x, in your question it is t).
in the above case all real numbers would satify the equation EXCEPT for x = 1, because at that point you have a 0 in your denominator.

you can think of domain (sort of) as "what input will make my function break the rules of artimatic.  my domain is everything except those numbers."

anonymous · Answer

are there any values of t that will make the cosine function break the rules of arithmatic (negative square roots, zeroes in denominators,etc etc)?

anonymous · Answer

is t going to be a degree or radian value?

anonymous · Answer

we use radian's about 99% of the time when we use trig functions.

anonymous · Answer

that doesnt answer my question..

anonymous · Answer

The domain are the x-values such that the function will have a finite real value. You can plug in basically anything as x, except the values that cause h(x) to become infinite.

In this case, since tan 0 = 0, then cot 0 = inf. Which means 0 is not included in the domain. And its equivalents, such as pi, 2pi, 3pi, 4pi etc. are also not included in the domain. So, the domain is all real numbers excluding multiples of pi.
h(x), on the other hand, can range anywhere from negative infinity to positive infinity. It has no limits to its values. Hence, the range is all real numbers.