Answer:
both = - [tex]\frac{\sqrt{2} }{2}[/tex]
Step-by-step explanation:
[tex]\frac{5\pi }{4}[/tex] is an angle in the 3rd quadrant where both sin and cos < 0
The related acute angle is [tex]\frac{\pi }{4}[/tex] , then
cos ([tex]\frac{5\pi }{4}[/tex] ) = - cos ([tex]\frac{\pi }{4}[/tex] ) = - [tex]\frac{1}{\sqrt{2} }[/tex] = - [tex]\frac{\sqrt{2} }{2}[/tex]
sin ( [tex]\frac{5\pi }{4}[/tex] ) = - sin ([tex]\frac{\pi }{4}[/tex] ) = - [tex]\frac{1}{\sqrt{2} }[/tex] = [tex]\frac{\sqrt{2} }{2}[/tex]
