[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]