At 270^@270∘ for a unit radius circle
color(white)("XXX")sin(270^@) = ("opposite")/("hypotenuse")XXXsin(270∘)=oppositehypotenuse
color(white)("XXXXXXXXX")=y/sqrt(x^2+y^2)XXXXXXXXX=y√x2+y2
color(white)("XXXXXXXXX")=(-1)/sqrt(0^2+(-1)^2)XXXXXXXXX=−1√02+(−1)2
color(white)("XXXXXXXXXX")=-1XXXXXXXXXX=−1
At -180^@−180∘ for a unit circle
color(white)("XXX")cos(-180^@) = ("adjacent")/("hypotenuse")XXXcos(−180∘)=adjacenthypotenuse
(arguing similar to above)
color(white)("XXXXXXXXXX")= -1XXXXXXXXXX=−1
sin(270^@)+cos(-180^@) = (-1)+(-1) = -2sin(270∘)+cos(−180∘)=(−1)+(−1)=−2