Finding domain and range of vector functions

[year12issoohard]

can anyone help me with the domain and range of its cartesian equation:
r(t) = cot(2t) i  + 3cosec(2t) j , 0<= t <= pie/4
Thank you!

[brightsky]

x = cot(2t)
y = 3 cosec(2t)

Assuming that t ≥ 0, cot(2t) ∈ R and 3 cosec(2t) ∈ (-∞, -3] U [3, +∞). (Hint: Consider the graphs of cot(2t) and 3 cosec(2t).) Hence, domain is R and range is (-∞, -3] U [3, +∞).

[year12issoohard]

x = cot(2t)
y = 3 cosec(2t)

Assuming that t ≥ 0, cot(2t) ∈ R and 3 cosec(2t) ∈ (-∞, -3] U [3, +∞). (Hint: Consider the graphs of cot(2t) and 3 cosec(2t).) Hence, domain is R and range is (-∞, -3] U [3, +∞).

what will it be if the range of t is from 0 to pie/4 (inclusive)? sorry i forgot to write it down in the first place 

[keltingmeith]

what will it be if the range of t is from 0 to pie/4 (inclusive)? sorry i forgot to write it down in the first place 

Give what brighteye wrote a closer look - try copying that, but for your t instead of t>=0. Remember that the domain is the possible x values and the range is the possible y values.