C4 parametric domain

A curve has parametric equations

x = 2\cot t, y = 2\sin^{2}t, 0 < t\leq \frac{\pi}{2}

. Find a cartesian equation of the form and state the domain on which the curve is defined.

I've found the cartesian equation

\displaystyle y = \frac{8}{x^{2}+4}

.

Now here's where my problem lies - my teacher said that the curve is valid for all real values for

x

and he docked a mark at first, but clearly the range of

t

being restricted would mean that this can't hold true. He later took a look at the problem and he later agreed with me.

Wouldn't the domain be

x \geq 0, x \in \mathbb{R}

? This is what I initially wrote on my paper.

Wouldn't the domain be

x \geq 0, x \in \mathbb{R}

? This is what I initially wrote on my paper.

Yep, that's fine. :yep:

(edited 7 years ago)

if you look at this graph you can see that you are right....

Not greater than or equal to - strict inequality. But otherwise - yeah.

Why strict? I thought we're letting

t = \frac{\pi}{2}

\cot t

can be 0?

if you look at this graph you can see that you are right....

Thank you, this is how I looked at it initially.

Why strict? I thought we're letting

t = \frac{\pi}{2}

\cot t

can be 0?

Edited my answer before you replied. :tongue:

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