Question

Дано cosα=0,6; 3π/2<α<2π. Обчисліть cos(π/3-α)

Answer 1

$sin alpha =- sqrt{1-cos^2 alpha }=- sqrt{1- frac{9}{25} } =- sqrt{ frac{16}{25} } = -frac{4}{5} \ cos( frac{pi}{3}- alpha )=cosfrac{pi}{3}cos alpha +sinfrac{pi}{3}sin alpha \ = frac{1}{2} * frac{3}{5} - frac{ sqrt{3} }{2} * frac{4}{5} = frac{3}{10} - frac{4 sqrt{3} }{10} = frac{3-4 sqrt{3} }{10}$