How do evaluate sin 270 + cos (-180)?

1 Answer
Oct 1, 2015

sin(270^@)+cos(-180^@) = -2sin(270)+cos(180)=2

Explanation:

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=yx2+y2

color(white)("XXXXXXXXX")=(-1)/sqrt(0^2+(-1)^2)XXXXXXXXX=102+(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

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