With formula this gets hard

Calculus Level 2

If $C$ is the curve defined by $x(t)=\cos^2(t)$ and $y(t)=\sin^2(t)$ . The side length of $C$ for $t\in [0,\frac{\pi}{2}]$ is in the form $\sqrt{a}$ . Find the value of $a$

The answer is 2.

1 solution

Hjalmar Orellana Soto
Feb 21, 2016

As $y=sin^2(t) \rightarrow y=1-cos^2(t) \rightarrow y=1-x$ , as we want to know the side lenght for $t\in [0, \frac{\pi}{2}]$ , replacing in $x(t)$ we have that is the side lenght of $y=1-x$ for $x \in [0,1]$ so it is $\sqrt2$

With formula this gets hard

The answer is 2.

1 solution

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