MathDB

Trig Sum

Source:

December 18, 2005

trigonometryvectornumber theoryrelatively primetrig identities

Problem Statement

Given that

\sum_{k=1}^{35}\sin 5k=\tan \frac mn,

where angles are measured in degrees, and

m

and

n

are relatively prime positive integers that satisfy

\frac mn<90,

find

m+n.