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

1 Answer

Oct 1, 2015

$sin (270^{\circ}) + cos (- 180^{\circ}) = - 2$ $sin(270^@)+cos(-180^@) = -2$

Explanation:

At $270^{\circ}$ $270^@$ for a unit radius circle
$XXX sin (270^{\circ}) = \frac{opposite}{hypotenuse}$ $color(white)("XXX")sin(270^@) = ("opposite")/("hypotenuse")$

$XXXXXXXXX = \frac{y}{\sqrt{x^{2} + y^{2}}}$ $color(white)("XXXXXXXXX")=y/sqrt(x^2+y^2)$

$XXXXXXXXX = \frac{- 1}{\sqrt{0^{2} + {(- 1)}^{2}}}$ $color(white)("XXXXXXXXX")=(-1)/sqrt(0^2+(-1)^2)$

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

At $- 180^{\circ}$ $-180^@$ for a unit circle
$XXX cos (- 180^{\circ}) = \frac{adjacent}{hypotenuse}$ $color(white)("XXX")cos(-180^@) = ("adjacent")/("hypotenuse")$

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

$sin (270^{\circ}) + cos (- 180^{\circ}) = (- 1) + (- 1) = - 2$ $sin(270^@)+cos(-180^@) = (-1)+(-1) = -2$

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