Buktikan bahwa Sin(90°-teta)=cos teta.... Question from @cindy12

October 2018 2 27 Report

Buktikan bahwa Sin(90°-teta)=cos teta

ImmanuelSinaga $$\begin{align}sin~(90~-~\alpha)~~&=~~sin~90~cos~\alpha~-~cos~90~sin~\alpha \\ \bold{ingat~nilai~cos~90~=~NOL}~ \\ \bold{sin~90~=~SATU}\\ &=~~Sin~90~cos~\alpha \\ &=~~\bold{Cos~\alpha}\end{align}$

3 votes Thanks 3

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Takamori37 Cara 1 (Awal)
Dengan cara segitiga siku-siku (cek lampiran)
sin(90-Θ) = x/r
cos Θ = x/r

Tentu keduanya sama, sehingga terbukti.

Cara 2 (Lanjutan)
Untuk trigonometri yang lebih lanjut, akan memperkenalkan rumus berikut:
$\boxed{\sin(A-B)=\sin A\cos B-\cos A\sin B}$

Sehingga:
$$\begin{align}\sin(90-\theta)&=\cos\theta \\ \sin90\cos\theta-\cos90\sin\theta&=\cos\theta \\ 1.\cos\theta-0.\sin\theta&=\cos\theta \\ \cos\theta&=\cos\theta\end{align}$

1 votes Thanks 2

romayuli05 sin ( 90- teta) = cos teta sin 90 cos teta - cos 90 sin teta. ingat kalau sin 90= 1 dan cos 90 =0 1.cos teta -0.sin teta =cos teta cos teta= cos teta

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