Levi Rizki Saputra Notes

Sudut Komplemen

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# Dari Definisi Segitiga Siku-Siku

Sudut Komplemen

sin(θ)=BCACcos(θ)=ABACtan(θ)=BCABsin(90°θ)=ABACcos(90°θ)=BCACtan(90°θ)=ABBCsin(θ)=cos(90°θ)cos(θ)=sin(90°θ)tan(θ)=1(ABBC)=1tan(90°θ)\begin{align*} \sin(\theta) & =\frac{BC}{AC}\\ \cos(\theta) & =\frac{AB}{AC}\\ \tan(\theta) & =\frac{BC}{AB}\\ \sin(90\degree-\theta) & =\frac{AB}{AC}\\ \cos(90\degree-\theta) & =\frac{BC}{AC}\\ \tan(90\degree-\theta) & =\frac{AB}{BC}\\ \sin(\theta) & =\cos(90\degree-\theta)\\ \cos(\theta) & =\sin(90\degree-\theta)\\ \tan(\theta) & =\frac{1}{(\dfrac{AB}{BC})}\\ & =\frac{1}{\tan(90\degree-\theta)} \end{align*}

# Kesimpulan

Untuk θ\theta sudut apapun:

sin(θ)=cos(90°θ)cos(θ)=sin(90°θ)tan(θ)=1tan(90°θ)\begin{align*} \sin(\theta) &=\cos(90\degree-\theta)\\ \cos(\theta) &=\sin(90\degree-\theta)\\ \tan(\theta) &=\dfrac{1}{\tan(90\degree-\theta)}\\ \end{align*}