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Question
If sinθ1+sinθ2+sinθ3=3
find cosθ1+cosθ2+cosθ3

This is sort of a clever question. Since, for any θ, sinθ ≤ 1, the only way for sinθ1 + sinθ2 + sinθ3 = 3 is if θ1 = θ2 = θ3 = ±π/2, which means that cosθ1 = cosθ2 = cosθ3 = cos(±π/2) = 0, or

cosθ1 + cosθ2 + cosθ3 = 0.

Volunteer

#### randy patton

##### Expertise

college mathematics, applied math, advanced calculus, complex analysis, linear and abstract algebra, probability theory, signal processing, undergraduate physics, physical oceanography

##### Experience

26 years as a professional scientist conducting academic quality research on mostly classified projects involving math/physics modeling and simulation, data analysis and signal processing, instrument development; often ocean related

Publications
J. Physical Oceanography, 1984 "A Numerical Model for Low-Frequency Equatorial Dynamics", with M. Cane

Education/Credentials
M.S. MIT Physical Oceanography, B.S. UC Berkeley Applied Math

Past/Present Clients
Also an Expert in Oceanography