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MATH / While finding the sine of a certain angle, an absent-minded professor failed to…

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problem

While finding the sine of a certain angle, an absent-minded professor failed to notice that his calculator was not in the correct angular mode. He was lucky to get the right answer. The two least positive real values of xx for which the sine of xx degrees is the same as the sine of xx radians are mπn−π\frac{m\pi}{n-\pi} and pπq+π\frac{p\pi}{q+\pi}, where mm, nn, pp, and qq are positive integers. Find m+n+p+qm+n+p+q.
Plain-text mathematical notation (without MathML)
While finding the sine of a certain angle, an absent-minded professor failed to notice that his calculator was not in the correct angular mode. He was lucky to get the right answer. The two least positive real values of x for which the sine of x degrees is the same as the sine of x radians are (mπ)/(n−π) and (pπ)/(q+π), where m, n, p, and q are positive integers. Find m+n+p+q.
Original LaTeX notation
While finding the sine of a certain angle, an absent-minded professor failed to notice that his calculator was not in the correct angular mode. He was lucky to get the right answer. The two least positive real values of $x$ for which the sine of $x$ degrees is the same as the sine of $x$ radians are $\frac{m\pi}{n-\pi}$ and $\frac{p\pi}{q+\pi}$, where $m$, $n$, $p$, and $q$ are positive integers. Find $m+n+p+q$.

level

Level 3

type

Precalculus

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Source and history

task_id
4b639656-7542-53c0-9fba-f3b320aac570
task_key
precalculus--test--4b639656-7542-53c0-9fba-f3b320aac570
task_revision_id
1
config / split
precalculus / test

Official source

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