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    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.
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    (Original post by Ayman!)

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

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    (Original post by Zacken)
    Not greater than or equal to - strict inequality. But otherwise - yeah.

    Why strict? I thought we're letting t = \frac{\pi}{2} so \cot t can be 0?

    (Original post by the bear)
    if you look at this graph you can see that you are right....
    Thank you, this is how I looked at it initially.
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    (Original post by Ayman!)
    Why strict? I thought we're letting t = \frac{\pi}{2} so \cot t can be 0?
    Edited my answer before you replied.
 
 
 
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