I'm doing this question and I found out why a, b, and c can't be the answer. What about d, and e? I don't understand them. P.S the right answer is d :) Thank you very much.
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1There is not even an angle whose sine is $\pi$, since $\pi$ is too big. – André Nicolas Dec 19 '13 at 02:14
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$\sin^{-1}(\pi)$ in words means the angle whose sine is $\pi$. If $\frac{opposite}{hypotenuse} = \pi$, then the angle whose sides have that ratio would most certainly not be zero.
$\cos^{-1}(1)$ in words means the angle whose cosine is $1$. This is always going to be 0.
okarin
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Note that, like @okarin says, $\sin^{-1}(\pi)$ is the angle whose sine is $\pi$. Think about what you know about $\sin(x)$ though. What is the minimum value $\sin(x)$ can be? What is the maximum value $\sin(x)$ can be? (Hover over the box below for the answers.)
The minimum value of $\sin(x)$ is $-1$. The maximum value of $\sin(x)$ is $1$.
Now, we know that $\pi \approx 3.14\ldots$. Using this and the maximum value of $\sin(x)$, what can you say?
We know that there does not exist an angle whose sine is $\pi$ since $\pi>1$ and $1$ is the maximum value $\sin(x)$ can be.
Tyler Clark
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