Sudut Negatif

Konsep Dasar

Sudut negatif diasumsikan pada kuadran 4.

 

\(\sin (- \alpha) = - \sin \alpha\)

Sinus sudut pada kuadran 4 bernilai negatif.

 

\(\cos (- \alpha) = \cos \alpha \)

Cosinus sudut pada kuadran 4 bernilai positif.

 

\(\tan (- \alpha) = - \tan \alpha \)

Tangen sudut pada kuadran 4 bernilai negatif.

Contoh 1

\begin{equation*}
\begin{split}
\sin (-240^{\text{o}}) & = -\sin 240^{\text{o}} \\\\
\sin (-240^{\text{o}}) & = - \sin (180^{\text{o}} + 60^{\text{o}}) \\\\
\sin (-240^{\text{o}}) & = - (-\sin 60^{\text{o}}) \\\\
\sin (-240^{\text{o}}) & = \sin 60^{\text{o}} \\\\
\sin (-240^{\text{o}}) & = \frac{1}{2} \sqrt{3}
\end{split}
\end{equation*}

 

Contoh 2

\begin{equation*}
\begin{split}
\cos (-135^{\text{o}}) & = +\cos 135^{\text{o}} \\\\
\cos (-135^{\text{o}}) & = \cos (180^{\text{o}} - 45^{\text{o}}) \\\\
\cos (-135^{\text{o}}) & = -\cos 45^{\text{o}}  \\\\
\cos (-135^{\text{o}}) & = -\frac{1}{2} \sqrt{2}
\end{split}
\end{equation*}

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