Question

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

Answer 1

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

Explanation:

At `270^@` for a unit radius circle
`color(white)("XXX")sin(270^@) = ("opposite")/("hypotenuse")`

`color(white)("XXXXXXXXX")=y/sqrt(x^2+y^2)`

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

`color(white)("XXXXXXXXXX")=-1`

At `-180^@` for a unit circle
`color(white)("XXX")cos(-180^@) = ("adjacent")/("hypotenuse")`

(arguing similar to above)
`color(white)("XXXXXXXXXX")= -1`

`sin(270^@)+cos(-180^@) = (-1)+(-1) = -2`