HOTS Zone : Trigonometri

Berikut ini adalah kumpulan soal mengenai Trigonometri. Jika ingin bertanya soal, silahkan gabung ke grup Telegram, Signal, Discord, atau WhatsApp.

Tipe:

Standar SBMPTN HOTS

No.

Pada suatu tempat matahari tepat di atas benda (tanpa bayangan) pukul 11.55. Fulan melaksanakan sholat dzuhur ketika panjang bayangan benda \dfrac34 dari tinggi bendanya. Jam berapakah Fulan menunaikan sholat dzuhur?

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Kecepatan rotasi matahari :
$\begin{array}{rl}\omega & ={360}^{\circ }/24\text{ jam}\\ & ={15}^{\circ }/\text{jam}\\ & ={15}^{\circ }/60\text{ menit}\\ & 0,{25}^{\circ }/\text{menit}\end{array}$

$\begin{array}{rl}\tan \theta & ={\displaystyle \frac{3}{4}}\\ \theta & ={37}^{\circ }\end{array}$

\dfrac{37}{0{,}25}=148\text{ menit}=2\text{ jam }28\text{ menit}

11.55+02.28=14.23

Jadi, Fulan menunaikan sholat dzuhur pukul 14.23.

No.

\cos^2 41\degree + \cos^2 43\degree + \cos^2 45\degree + \cos^2 47\degree + \cos^2 49\degree = ....

1. 1
2. 1{,}5
3. 2

4. 2{,}5
5. 5

Learncy.net

$$\begin{array}{rl}{\cos }^{2}41{}^{\circ }+{\cos }^{2}43{}^{\circ }+{\cos }^{2}45{}^{\circ }+{\cos }^{2}47{}^{\circ }+{\cos }^{2}49{}^{\circ }& ={\cos }^{2}41{}^{\circ }+{\cos }^{2}43{}^{\circ }+{\left({\displaystyle \frac{1}{2}}\sqrt{2}\right)}^2+{\sin }^{2}43{}^{\circ }+{\sin }^{2}41{}^{\circ }\\ & ={\cos }^{2}41{}^{\circ }+{\sin }^{2}41{}^{\circ }+{\cos }^{2}43{}^{\circ }+{\sin }^{2}43{}^{\circ }+{\displaystyle \frac{1}{4}}\cdot 2\\ & =1+1+{\displaystyle \frac{1}{2}}\\ & =2,5\end{array}$$

Jadi, \cos^2 41\degree + \cos^2 43\degree + \cos^2 45\degree + \cos^2 47\degree + \cos^2 49\degree =2{,}5. JAWAB: D