If cos(Ɵ)=7/8 andƟ is in the 1st quadrant, then what is sin(Ɵ) ?

square root of fifteen over eight.

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Do a simple sketch with theta in Quad 1 and cos theta = 7/8 i.e. Adj = 7, hypot.= 8 so Opp = sqrt (8^2 - 7^2) = sqrt64 - 49 = sqrt 15, so sin theta = Opp/Hypot = sqrt(15)/8