[latex]cos ( alpha + frac{ pi }{4} ), cos alpha = -frac{3}{5} [/latex]

[latex] cos alpha =- frac{3}{5}; \ sin alpha = sqrt{1-cos^2 alpha }= sqrt{1- frac{9}{25}}= sqrt{ frac{16}{25}}= frac{4}{5}; \ cos( alpha + frac{pi }{4})= cos alpha *cos frac{ pi }{4}-sin alpha *sin frac{ pi }{4}=- frac{3}{5}* frac{ sqrt{2} }{2}- frac{4}{5}* frac{ sqrt{2} }{2}= -frac{7 sqrt{2} }{10}. [/latex]