<s>[INST] How to obtain $y$ 
The question was written with dark-blue pen. And I tried to solve this question. I obtained $x$ as it is below.  But I cannot obtain $y$  Please show me how to do this. 
By the way, $\gamma (t)$ may not be clearly readable. So, I wrote again. 
$$\gamma (t)=( \cos ^2 (t)-1/2, \sin(t)\cos (t), \sin (t))$$
Thanks for helping. 
-sorry for not writing with MathJax. -
 [/INST] From your work,
$$x^2+y^2=\frac{1}{4} \Rightarrow y^2=\frac{1}{4}-x^2,$$
and
$$x=\cos^2 t -\frac{1}{2}.$$
Substituting the latter into the former produces
\begin{align*}
y^2 &=\frac{1}{4}-x^2 \\
&=\frac{1}{4}-\left( \cos^2 t - \frac{1}{2} \right)^2 \\
&=\frac{1}{4}-\left( \cos^4 t - \cos^2 t + \frac{1}{4} \right) \\
&=\cos^2 t - \cos^4 t \\
&=\cos^2 t\left( 1-\cos^2 t \right) \\
&=\cos^2 t \sin^2 t \\
\Rightarrow y &= \sin t \cos t,
\end{align*}
as was your intention.
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