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Q: Current value of $\sin(3^{1/5})$ when value of $3^{1/5} = 3^{(1/5)}$? Just a simple question that I can’t seem to figure out. $\sin(3^{1/5})$ What is the value of $\sin(3^{1/5})$ if $\sin(x^{1/n})$ is defined as $\sin(x)$ when $x$ is an integer multiple of $2\pi n$? A: There are two cases to consider: $n$ odd and $n$ even. Let’s make a function $f:\mathbb{R}_+\to\mathbb{R}$ given by $f(t)=\sin(t^{1/n})$. This function has a fixed point in the positive real numbers, namely $t=\pi/n$ (it’s easy to check that it’s in the domain of $f$). Thus, by the intermediate value theorem, we conclude that $\sin(3^{1/5})$ is in the interval $(-0.5,0.5)$, namely $\sin(3^{1/5})=\pm0.4659$. Now, the same reasoning applies if $n$ is odd, so we get the same solution. And if $n$ is even, we have $t=3\pi/2n$, and thus $\sin(t^{1/n})=\sin(3\pi/2n)=0$, which gives us another solution, namely $\sin(3^{1/5})=0.3210$. Q: Facebook like button I need a Facebook Like Button on my website. I have copied the code below from Facebook. I am using a codeigniter framework. I have added the file to the template and then added the following code. #fb-root { overflow: hidden; } #fb-root iframe { position:
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