Emmanuel Pace

2022-07-18

How do you find the exact value of $\mathrm{cos}$ 180 degrees - $\mathrm{sin}$ 180 degrees?

grocbyntza

Expert

Within the unit circle, cosine provides the x coordinate of a point on the surface of the circle. Sine provides the y coordinate of a point on the surface of the circle.
At ${180}^{\circ }$, the point on the unit circle surface is (-1,0). So this means:
$x=\mathrm{cos}\left({180}^{\circ }\right)=-1$
$y=\mathrm{sin}\left({180}^{\circ }\right)=0$
To find the exact value of $\mathrm{cos}\left({180}^{\circ }\right)-\mathrm{sin}\left({180}^{\circ }\right)$
-1-0=-1

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