Properties of Trigonometry
Geometry
Level
3
Find the exact value of cos(1) + cos(2) + cos(3) + ... + cos(357) + cos(358) + cos(359)
Note: all angles measured in degrees
The answer is -1.
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1 solution
Since cos(x) + cos(180 + x) = 0, then cos(1) + cos(180+1) = 0, cos(2) + cos(180+2) = 0, and so forth. Thus cos(180) is the only term without an opposite "partner", leaving cos(180) as the only term left with no one to dance with :( ... and therefore the answer is cos(180) = -1