A geometry problem by Chandrashekar Giridharan

Geometry Level 2

cosθ+cos(θ+1)+cos(θ+2)++cos(θ+359)\cos \theta^\circ + \cos (\theta^\circ+1^\circ) + \cos (\theta^\circ+2^\circ) +\cdots + \cos (\theta^\circ+359^\circ)

What is the value of this expression when θ\theta is an integer?

A certain theta value is shown here, but theta can be any integer. Consider how the cosine changes as the angle increases. A certain theta value is shown here, but theta can be any integer. Consider how the cosine changes as the angle increases.

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