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Dear Students,
Welcome to today’s quiz! This is your opportunity to demonstrate what you’ve learned so far, so do your best. Please keep in mind that you have a maximum of 30 minutes to complete all the questions. Make sure to manage your time wisely and answer each question thoughtfully.
Good luck!
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Pertanyaan 1 dari 30
1. Pertanyaan
1 points\(1\frac{4}{5}\pi\) radian = … °
Benar
\(1\frac{4}{5}\pi\) radian = \(\frac{9}{5}\pi \times \color{red} \frac{180^{\circ}}{\pi} \color{black} = 324^{\circ}\)
Salah
\(1\frac{4}{5}\pi\) radian = \(\frac{9}{5}\pi \times \color{red} \frac{180^{\circ}}{\pi} \color{black} = 324^{\circ}\)
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Pertanyaan 2 dari 30
2. Pertanyaan
1 points\(216^{\circ} = \dotso \text{ radian}\)
Benar
\(216^{\circ} = 216^{\circ} \times \color{red} \frac{\pi}{180^{\circ}}\color{black} = 1\frac{1}{5}\pi\text{ rad }\)
Salah
\(216^{\circ} = 216^{\circ} \times \color{red} \frac{\pi}{180^{\circ}}\color{black} = 1\frac{1}{5}\pi\text{ rad }\)
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Pertanyaan 3 dari 30
3. Pertanyaan
1 pointsPerhatikan segitiga siku-siku berikut:
Nilai \(\cos \alpha \times \cot \alpha = \dotso\)
Benar
Mencari panjang sisi samping:
\(x^2 + (\sqrt{2})^2 = 5^2\)
\(x^2 + 2 = 25\)
\(x^2 = 25\:-\:2\)
\(x^2 = 23\)
\(x = \sqrt{23}\)
\(\cos \alpha \times \cot \alpha\)
\(\frac{\text{samping}}{\text{miring}}\times \frac{\text{samping}}{\text{depan}}\)
\(\frac{\sqrt{23}}{5}\times \frac{\sqrt{23}}{\sqrt{2}}\)
\(\frac{23}{5\sqrt{2}}\times \color{red}\frac{\sqrt{2}}{\sqrt{2}}\)
\(\frac{23}{10}\sqrt{2}\)
Salah
Mencari panjang sisi samping:
\(x^2 + (\sqrt{2})^2 = 5^2\)
\(x^2 + 2 = 25\)
\(x^2 = 25\:-\:2\)
\(x^2 = 23\)
\(x = \sqrt{23}\)
\(\cos \alpha \times \cot \alpha\)
\(\frac{\text{samping}}{\text{miring}}\times \frac{\text{samping}}{\text{depan}}\)
\(\frac{\sqrt{23}}{5}\times \frac{\sqrt{23}}{\sqrt{2}}\)
\(\frac{23}{5\sqrt{2}}\times \color{red}\frac{\sqrt{2}}{\sqrt{2}}\)
\(\frac{23}{10}\sqrt{2}\)
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Pertanyaan 4 dari 30
4. Pertanyaan
1 pointsHasil dari \(\dfrac{\sin 60^{\circ}\cdot \cos 45^{\circ}\:-\:\cos 60^{\circ}\cdot \sin 45^{\circ}}{\tan 60^{\circ}} = \dotso\)
Benar
\(\dfrac{\frac{1}{2}\sqrt{3}\cdot \frac{1}{2}\sqrt{2}\:-\:\frac{1}{2}\cdot \frac{1}{2}\sqrt{2}}{\sqrt{3}} \)
\(\dfrac{\frac{1}{4}\sqrt{6}\:-\:\frac{1}{4}\sqrt{2}}{\sqrt{3}}\times \color{red}\dfrac{\sqrt{3}}{\sqrt{3}}\)
\(\dfrac{\frac{1}{4}\sqrt{18}\:-\:\frac{1}{4}\sqrt{6}}{3}\)
\(\frac{1}{12}\sqrt{18}\:-\:\frac{1}{12}\sqrt{6}\)
\(\frac{3}{12}\sqrt{2}\:-\:\frac{1}{12}\sqrt{6}\)
\(\frac{1}{4}\sqrt{2}\:-\:\frac{1}{12}\sqrt{6}\)
Salah
\(\dfrac{\frac{1}{2}\sqrt{3}\cdot \frac{1}{2}\sqrt{2}\:-\:\frac{1}{2}\cdot \frac{1}{2}\sqrt{2}}{\sqrt{3}} \)
\(\dfrac{\frac{1}{4}\sqrt{6}\:-\:\frac{1}{4}\sqrt{2}}{\sqrt{3}}\times \color{red}\dfrac{\sqrt{3}}{\sqrt{3}}\)
\(\dfrac{\frac{1}{4}\sqrt{18}\:-\:\frac{1}{4}\sqrt{6}}{3}\)
\(\frac{1}{12}\sqrt{18}\:-\:\frac{1}{12}\sqrt{6}\)
\(\frac{3}{12}\sqrt{2}\:-\:\frac{1}{12}\sqrt{6}\)
\(\frac{1}{4}\sqrt{2}\:-\:\frac{1}{12}\sqrt{6}\)
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Pertanyaan 5 dari 30
5. Pertanyaan
1 pointsHasil dari \(\csc 30^{\circ}\cdot \sec 45^{\circ} + \cos 90^{\circ}\cdot \tan 19^{\circ} = \dotso\)
Benar
\(\csc 30^{\circ}\cdot \sec 45^{\circ} + \cos 90^{\circ}\cdot \tan 19^{\circ}\)
\(2\cdot \sqrt{2} + 0\)
\(2\sqrt{2}\)
Salah
\(\csc 30^{\circ}\cdot \sec 45^{\circ} + \cos 90^{\circ}\cdot \tan 19^{\circ}\)
\(2\cdot \sqrt{2} + 0\)
\(2\sqrt{2}\)
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Pertanyaan 6 dari 30
6. Pertanyaan
1 points\(1\frac{1}{2}\pi \text{ radian} = \dotso ^{\circ}\)
Benar
\(1\frac{1}{2}\pi \text{ radian} = \frac{3}{2}\pi \times \frac{180^{\circ}}{\pi}\)
\(1\frac{1}{2}\pi \text{ radian} = 270^{\circ}\)
Salah
\(1\frac{1}{2}\pi \text{ radian} = \frac{3}{2}\pi \times \frac{180^{\circ}}{\pi}\)
\(1\frac{1}{2}\pi \text{ radian} = 270^{\circ}\)
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Pertanyaan 7 dari 30
7. Pertanyaan
1 points\(1\text{ radian} = \dotso ^{\circ}\)
Benar
\(1\text{ radian} = \frac{180 ^{\circ}}{\pi}\)
\(1\text{ radian} = \frac{180 ^{\circ}}{\frac{22}{7}} = 57,27^{\circ}\)
Salah
\(1\text{ radian} = \frac{180 ^{\circ}}{\pi}\)
\(1\text{ radian} = \frac{180 ^{\circ}}{\frac{22}{7}} = 57,27^{\circ}\)
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Pertanyaan 8 dari 30
8. Pertanyaan
1 points\(1^{\circ} = \dotso \text{ radian}\)
Benar
\(1^{\circ} = \frac{\pi}{180^{\circ}} \text{ radian}\)
Salah
\(1^{\circ} = \frac{\pi}{180^{\circ}} \text{ radian}\)
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Pertanyaan 9 dari 30
9. Pertanyaan
1 points\(150^{\circ} = \dotso \text{ radian}\)
Benar
\(150^{\circ} = 150^{\circ}\times \frac{\pi}{180^{\circ}} \text{ radian}\)
\(150^{\circ} = \frac{5}{6}\pi\text{ radian}\)
Salah
\(150^{\circ} = 150^{\circ}\times \frac{\pi}{180^{\circ}} \text{ radian}\)
\(150^{\circ} = \frac{5}{6}\pi\text{ radian}\)
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Pertanyaan 10 dari 30
10. Pertanyaan
1 pointsPerhatikan segitiga siku-siku berikut:
Nilai \(\sin \alpha + \csc \alpha = \dotso\)
Benar
Menentukan panjang sisi depan,
\(x^2 + (\sqrt{15})^2 = 4^2\)
\(x^2 + 15 = 16\)
\(x^2 = 1\)
\(x = 1\)
\(\sin \alpha + \csc \alpha\)
\(\frac{1}{4} + \frac{4}{1} = 4\frac{1}{4}\)
Salah
Menentukan panjang sisi depan,
\(x^2 + (\sqrt{15})^2 = 4^2\)
\(x^2 + 15 = 16\)
\(x^2 = 1\)
\(x = 1\)
\(\sin \alpha + \csc \alpha\)
\(\frac{1}{4} + \frac{4}{1} = 4\frac{1}{4}\)
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Pertanyaan 11 dari 30
11. Pertanyaan
1 pointsPerhatikan segitiga siku-siku berikut:
Jika \(\csc \alpha = \dfrac{\sqrt{3}}{5}\), maka nilai \(x\) adalah …
Benar
\(\csc \alpha = \dfrac{\sqrt{3}}{5}\)
\(\sin\alpha = \dfrac{5}{\sqrt{3}}\)
\(\dfrac{x}{10\sqrt{3}} = \dfrac{5}{\sqrt{3}}\)
\(x = \dfrac{5}{\cancel{\sqrt{3}}}\times 10\cancel{\sqrt{3}}\)
\(x = 50\)
Salah
\(\csc \alpha = \dfrac{\sqrt{3}}{5}\)
\(\sin\alpha = \dfrac{5}{\sqrt{3}}\)
\(\dfrac{x}{10\sqrt{3}} = \dfrac{5}{\sqrt{3}}\)
\(x = \dfrac{5}{\cancel{\sqrt{3}}}\times 10\cancel{\sqrt{3}}\)
\(x = 50\)
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Pertanyaan 12 dari 30
12. Pertanyaan
1 pointsPerhatikan segitiga siku-siku berikut!
Jika \(\alpha = 30^{\circ}\), maka nilai \(x = \dotso\)
Benar
Perhatikan segitiga siku-siku yang besar,
\(\sin 30^{\circ} = \dfrac{y}{48}\)
\(\dfrac{1}{2} = \dfrac{y}{48}\)
\(y = 24\)
Lihat segitiga kecil dan tentukan nilai \(x\) menggunakan rumus pythagoras,
\(x^2 + 24^2 = 25^2\)
\(x^2 + 576 = 625\)
\(x^2 = 49\)
\(x = 7\)
Salah
Perhatikan segitiga siku-siku yang besar,
\(\sin 30^{\circ} = \dfrac{y}{48}\)
\(\dfrac{1}{2} = \dfrac{y}{48}\)
\(y = 24\)
Lihat segitiga kecil dan tentukan nilai \(x\) menggunakan rumus pythagoras,
\(x^2 + 24^2 = 25^2\)
\(x^2 + 576 = 625\)
\(x^2 = 49\)
\(x = 7\)
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Pertanyaan 13 dari 30
13. Pertanyaan
1 pointsPerhatikan gabungan segitiga siku-siku berikut!
Jika panjang AB = \(5\sqrt{3}\) cm, maka panjang EC = … cm
Benar
Lihat ΔDAB,
\(\cos 30^{\circ} = \dfrac{\text{AB}}{\text{BD}}\)
\(\dfrac{\sqrt{3}{2}} = \dfrac{5\sqrt{3}}{\text{BD}}\)
\(\dfrac{\cancel{\sqrt{3}}}{2} = \dfrac{5\cancel{\sqrt{3}}}{\text{BD}}\)
\(\text{BD} = 10\)
Lihat ΔBDE,
\(\cos 30^{\circ} = \dfrac{\text{BD}}{\text{BE}}\)
\(\dfrac{\sqrt{3}}{2} = \dfrac{10}{\text{BE}}\)
\(\sqrt{3}\text{BE} = 20\)
\(\text{BE} = \dfrac{20}{\sqrt{3}}\)
Lihat ΔBCE,
\(\sin 30^{\circ} = \dfrac{\text{EC}}{\text{BE}}\)
\(\dfrac{1}{2} = \dfrac{\text{EC}}{\dfrac{20}{\sqrt{3}}}\)
\(\text{EC} = \dfrac{10}{\sqrt{3}}\)
\(\text{EC} = \dfrac{10}{3}\sqrt{3}\)
Salah
Lihat ΔDAB,
\(\cos 30^{\circ} = \dfrac{\text{AB}}{\text{BD}}\)
\(\dfrac{\sqrt{3}{2}} = \dfrac{5\sqrt{3}}{\text{BD}}\)
\(\dfrac{\cancel{\sqrt{3}}}{2} = \dfrac{5\cancel{\sqrt{3}}}{\text{BD}}\)
\(\text{BD} = 10\)
Lihat ΔBDE,
\(\cos 30^{\circ} = \dfrac{\text{BD}}{\text{BE}}\)
\(\dfrac{\sqrt{3}}{2} = \dfrac{10}{\text{BE}}\)
\(\sqrt{3}\text{BE} = 20\)
\(\text{BE} = \dfrac{20}{\sqrt{3}}\)
Lihat ΔBCE,
\(\sin 30^{\circ} = \dfrac{\text{EC}}{\text{BE}}\)
\(\dfrac{1}{2} = \dfrac{\text{EC}}{\dfrac{20}{\sqrt{3}}}\)
\(\text{EC} = \dfrac{10}{\sqrt{3}}\)
\(\text{EC} = \dfrac{10}{3}\sqrt{3}\)
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Pertanyaan 14 dari 30
14. Pertanyaan
1 pointsHasil dari \(\dfrac{\sin 30^{\circ}\cdot \cos 60^{\circ} + \cos 30^{\circ}\cdot \sin 60^{\circ}}{\tan 45^{\circ}} = \dotso\)
Benar
\(\dfrac{\frac{1}{2}\cdot \frac{1}{2} + \frac{1}{2}\sqrt{3}\cdot \frac{1}{2}\sqrt{3}}{1}\)
\(\frac{1}{4} + \frac{3}{4} = 1\)
Salah
\(\dfrac{\frac{1}{2}\cdot \frac{1}{2} + \frac{1}{2}\sqrt{3}\cdot \frac{1}{2}\sqrt{3}}{1}\)
\(\frac{1}{4} + \frac{3}{4} = 1\)
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Pertanyaan 15 dari 30
15. Pertanyaan
1 pointsHasil dari \(\dfrac{\csc 30^{\circ}\cdot \sec 60^{\circ} + \cot 30^{\circ}}{\sin 90^{\circ} + \cos 0^{\circ}} = \dotso\)
Benar
\(\dfrac{2\cdot 2 + \sqrt{3}}{1 + 1}\)
\(\dfrac{4 + \sqrt{3}}{2}\)
\(2 + \dfrac{1}{2}\sqrt{3}\)
Salah
\(\dfrac{2\cdot 2 + \sqrt{3}}{1 + 1}\)
\(\dfrac{4 + \sqrt{3}}{2}\)
\(2 + \dfrac{1}{2}\sqrt{3}\)
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Pertanyaan 16 dari 30
16. Pertanyaan
1 pointsHasil dari \(\dfrac{\tan \frac{1}{4}\pi + \cos \frac{1}{2}\pi \cdot \sin \frac{1}{3}\pi}{\csc \frac{1}{4}\pi} = \dotso\)
Benar
\(\dfrac{\tan 45^{\circ} + \cos 90^{\circ} \cdot \sin 60^{\circ}}{\csc 45^{\circ}}\)
\(\dfrac{1 + 0\cdot \frac{1}{2}\sqrt{3}}{\sqrt{2}}\)
\(\dfrac{1}{\sqrt{2}}\times \color{red} \dfrac{\sqrt{2}}{\sqrt{2}}\)
\(\dfrac{1}{2}\sqrt{2}\)
Salah
\(\dfrac{\tan 45^{\circ} + \cos 90^{\circ} \cdot \sin 60^{\circ}}{\csc 45^{\circ}}\)
\(\dfrac{1 + 0\cdot \frac{1}{2}\sqrt{3}}{\sqrt{2}}\)
\(\dfrac{1}{\sqrt{2}}\times \color{red} \dfrac{\sqrt{2}}{\sqrt{2}}\)
\(\dfrac{1}{2}\sqrt{2}\)
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Pertanyaan 17 dari 30
17. Pertanyaan
1 pointsHasil dari \(\sin^2 30^{\circ} + \cos^2 30^{\circ}\) adalah …
Benar
\((\frac{1}{2})^2 + (\frac{1}{2}\sqrt{3})^2\)
\(\frac{1}{4} + \frac{3}{4} = 1\)
Salah
\((\frac{1}{2})^2 + (\frac{1}{2}\sqrt{3})^2\)
\(\frac{1}{4} + \frac{3}{4} = 1\)
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Pertanyaan 18 dari 30
18. Pertanyaan
1 pointsKoordinat polar dari titik \((2, 2\sqrt{3})\) adalah …
Benar
Koordinat polar = \((r, \theta)\)
\(r = \sqrt{x^2 + y^2}\)
\(r = \sqrt{2^2 + (2\sqrt{3})^2}\)
\(r = \sqrt{4 + 12}\)
\(r = \sqrt{16} = 4\)
\(\tan \theta = \frac{y}{x}\)
\(\tan \theta = \frac{2\sqrt{3}}{2} = \sqrt{3}\)
\(\theta = 60^{\circ}\)
Titik \((2, 2\sqrt{3})\) berada di kuadran I
Jadi kordinat polarnya adalah \((4, 60^{\circ})\)
Salah
Koordinat polar = \((r, \theta)\)
\(r = \sqrt{x^2 + y^2}\)
\(r = \sqrt{2^2 + (2\sqrt{3})^2}\)
\(r = \sqrt{4 + 12}\)
\(r = \sqrt{16} = 4\)
\(\tan \theta = \frac{y}{x}\)
\(\tan \theta = \frac{2\sqrt{3}}{2} = \sqrt{3}\)
\(\theta = 60^{\circ}\)
Titik \((2, 2\sqrt{3})\) berada di kuadran I
Jadi kordinat polarnya adalah \((4, 60^{\circ})\)
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Pertanyaan 19 dari 30
19. Pertanyaan
1 pointsKoordinat kartesius dari titik \((2\sqrt{3}, 60^{\circ})\) adalah …
Benar
\(x = r\cdot \cos \theta\)
\(x = 2\sqrt{3}\cdot \cos 60^{\circ}\)
\(x = 2\sqrt{3}\cdot \frac{1}{2} = \sqrt{3}\)
\(y = r\cdot \sin \theta\)
\(x = 2\sqrt{3}\cdot \sin 60^{\circ}\)
\(x = 2\sqrt{3}\cdot \frac{1}{2}\sqrt{3} = 3\)
Jadi koordinat kartesiusnya adalah \((\sqrt{3}, 3)\)
Salah
\(x = r\cdot \cos \theta\)
\(x = 2\sqrt{3}\cdot \cos 60^{\circ}\)
\(x = 2\sqrt{3}\cdot \frac{1}{2} = \sqrt{3}\)
\(y = r\cdot \sin \theta\)
\(x = 2\sqrt{3}\cdot \sin 60^{\circ}\)
\(x = 2\sqrt{3}\cdot \frac{1}{2}\sqrt{3} = 3\)
Jadi koordinat kartesiusnya adalah \((\sqrt{3}, 3)\)
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Pertanyaan 20 dari 30
20. Pertanyaan
1 pointsDiketahui koordinat polar dari titik \((x, 5)\) adalah \((r, 30^{\circ})\). Nilai \(x\) yang mungkin adalah …
Benar
\(y = r\cdot \sin \theta\)
\(5 = r\cdot \sin 30^{\circ}\)
\(5 = r\cdot \frac{1}{2}\)
\(r = 10\)
\(x = r\cdot \cos \theta\)
\(x = 10\cdot \cos 30^{\circ}\)
\(x = 10\cdot \frac{1}{2}\sqrt{3}\)
\(x = 5\sqrt{3}\)
Salah
\(y = r\cdot \sin \theta\)
\(5 = r\cdot \sin 30^{\circ}\)
\(5 = r\cdot \frac{1}{2}\)
\(r = 10\)
\(x = r\cdot \cos \theta\)
\(x = 10\cdot \cos 30^{\circ}\)
\(x = 10\cdot \frac{1}{2}\sqrt{3}\)
\(x = 5\sqrt{3}\)
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Pertanyaan 21 dari 30
21. Pertanyaan
1 pointsTitik P\((6, y)\) terletak di kuadran I, sudut yang dibentuk oleh sumbu x positif, titik asal (0, 0), dan titik P adalah \(\alpha\). Jika \(\sin \alpha = \frac{6}{10}\), maka nilai \(y\) adalah …
Benar
Menentukan sisi miring segitiga,
Panjang sisi miring = \(\sqrt{6^2 + y^2}\)
Panjang sisi miring = \(\sqrt{36 + y^2}\)
\(\sin \alpha = \dfrac{6}{10}\)
\(\dfrac{y}{\sqrt{36 + y^2}} = \dfrac{3}{5}\)
Kuadratkan kedua ruas,
\(\dfrac{y^2}{36 + y^2} = \dfrac{9}{25}\)
\(25y^2 = 9(36 + y^2)\)
\(25y^2 = 324 + 9y^2\)
\(25y^2\:-\:9y^2 = 324\)
\(16y^2 = 324\)
\(y^2 = \dfrac{324}{16}\)
\(y = \sqrt{\dfrac{324}{16}}\)
\(y = \dfrac{18}{4} = 4,5\)
Salah
Menentukan sisi miring segitiga,
Panjang sisi miring = \(\sqrt{6^2 + y^2}\)
Panjang sisi miring = \(\sqrt{36 + y^2}\)
\(\sin \alpha = \dfrac{6}{10}\)
\(\dfrac{y}{\sqrt{36 + y^2}} = \dfrac{3}{5}\)
Kuadratkan kedua ruas,
\(\dfrac{y^2}{36 + y^2} = \dfrac{9}{25}\)
\(25y^2 = 9(36 + y^2)\)
\(25y^2 = 324 + 9y^2\)
\(25y^2\:-\:9y^2 = 324\)
\(16y^2 = 324\)
\(y^2 = \dfrac{324}{16}\)
\(y = \sqrt{\dfrac{324}{16}}\)
\(y = \dfrac{18}{4} = 4,5\)
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Pertanyaan 22 dari 30
22. Pertanyaan
1 pointsTono mengamati puncak gedung dengan sudut elevasi \(30^{\circ}\). Jika Tono bergerak maju mendekati gedung sejauh 10 m, maka Tono akan melihat puncak gedung dengan sudut elevasi \(45^{\circ}\). Jika dianggap tinggi mata Tono 150 cm, maka tinggi gedung tersebut diukur dari permukaan tanah adalah …
Benar
\(\tan 30^{\circ} = \dfrac{y}{10 + y}\)
\(\dfrac{1}{\sqrt{3}}= \dfrac{y}{10 + y}\)
\(10 + y = \sqrt{3}y\)
\(10 = \sqrt{3}y\:-\:y\)
\(10 = y(\sqrt{3}\:-\:1)\)
\(y = \dfrac{10}{\sqrt{3}\:-\:1}\times \color{red} \dfrac{\sqrt{3} + 1}{\sqrt{3} + 1}\)
\(y = \dfrac{10\sqrt{3} + 10}{3\:-\:1}\)
\(y = \dfrac{10\sqrt{3} + 10}{2}\)
\(y = 5\sqrt{3} + 5 \text{ m}\)
Ketinggian gedung = \(y\) + tinggi mata Tono
Ketinggian gedung = \(5\sqrt{3} + 5 + 1,5 \text{ m}\)
Ketinggian gedung = \(6,5 + 5\sqrt{3}\text{ m}\)
Salah
\(\tan 30^{\circ} = \dfrac{y}{10 + y}\)
\(\dfrac{1}{\sqrt{3}}= \dfrac{y}{10 + y}\)
\(10 + y = \sqrt{3}y\)
\(10 = \sqrt{3}y\:-\:y\)
\(10 = y(\sqrt{3}\:-\:1)\)
\(y = \dfrac{10}{\sqrt{3}\:-\:1}\times \color{red} \dfrac{\sqrt{3} + 1}{\sqrt{3} + 1}\)
\(y = \dfrac{10\sqrt{3} + 10}{3\:-\:1}\)
\(y = \dfrac{10\sqrt{3} + 10}{2}\)
\(y = 5\sqrt{3} + 5 \text{ m}\)
Ketinggian gedung = \(y\) + tinggi mata Tono
Ketinggian gedung = \(5\sqrt{3} + 5 + 1,5 \text{ m}\)
Ketinggian gedung = \(6,5 + 5\sqrt{3}\text{ m}\)
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Pertanyaan 23 dari 30
23. Pertanyaan
1 pointsPernyataan di bawah ini yang salah adalah …
Benar
Salah
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Pertanyaan 24 dari 30
24. Pertanyaan
1 pointsPernyataan di bawah ini yang benar adalah …
Benar
Salah
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Pertanyaan 25 dari 30
25. Pertanyaan
1 pointsDiketahui \(\sin \alpha = 0,8\) dan \(\cos \beta = \frac{1}{3}\), dengan \(\alpha\) dan \(\beta\) sudut lancip. Nilai \(\tan \alpha \times \csc \beta\) adalah …
Benar
\(\sin \alpha = 0,8 = \frac{8}{10}\)
\(\tan \alpha = \frac{8}{6} = \frac{4}{3}\)
\(\cos \beta = \frac{1}{3}\)
\(\csc \beta = \frac{3}{2\sqrt{2}} = \frac{3\sqrt{2}}{4}\)
\(\tan \alpha \times \csc \beta\)
\(\frac{4}{3} \times \frac{3\sqrt{2}}{4}\)
\(\sqrt{2}\)
Salah
\(\sin \alpha = 0,8 = \frac{8}{10}\)
\(\tan \alpha = \frac{8}{6} = \frac{4}{3}\)
\(\cos \beta = \frac{1}{3}\)
\(\csc \beta = \frac{3}{2\sqrt{2}} = \frac{3\sqrt{2}}{4}\)
\(\tan \alpha \times \csc \beta\)
\(\frac{4}{3} \times \frac{3\sqrt{2}}{4}\)
\(\sqrt{2}\)
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Pertanyaan 26 dari 30
26. Pertanyaan
1 points\(\dfrac{1 + \cos 30^{\circ} + \cos 60^{\circ}}{\sin 60^{\circ} + \sin 30^{\circ}} = \dotso\)
Benar
\(\dfrac{1 + \frac{1}{2}\sqrt{3} + \frac{1}{2}}{\frac{1}{2}\sqrt{3} + \frac{1}{2}}\)
\(\dfrac{\frac{\sqrt{3} + 3}{2}}{\frac{\sqrt{3} + 1}{2}}\)
\(\dfrac{\sqrt{3} + 3}{\sqrt{3} + 1}\times \color{red} \dfrac{\sqrt{3} \:-\:1}{\sqrt{3} \:-\:1}\)
\(\dfrac{3\:-\:\sqrt{3} + 3\sqrt{3} \:-\:1}{3\:-\:1}\)
\(\dfrac{2\sqrt{3}}{2}\)
\(\sqrt{3} = \cot 30^{\circ}\)
Salah
\(\dfrac{1 + \frac{1}{2}\sqrt{3} + \frac{1}{2}}{\frac{1}{2}\sqrt{3} + \frac{1}{2}}\)
\(\dfrac{\frac{\sqrt{3} + 3}{2}}{\frac{\sqrt{3} + 1}{2}}\)
\(\dfrac{\sqrt{3} + 3}{\sqrt{3} + 1}\times \color{red} \dfrac{\sqrt{3} \:-\:1}{\sqrt{3} \:-\:1}\)
\(\dfrac{3\:-\:\sqrt{3} + 3\sqrt{3} \:-\:1}{3\:-\:1}\)
\(\dfrac{2\sqrt{3}}{2}\)
\(\sqrt{3} = \cot 30^{\circ}\)
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Pertanyaan 27 dari 30
27. Pertanyaan
1 pointsJika \(4\sin x \:-\:2\sqrt{2} = 0\), dengan \(x\) adalah sudut lancip, maka nilai \(\tan x = \dotso\)
Benar
\(4\sin x \:-\:2\sqrt{2} = 0\)
\(4\sin x = 2\sqrt{2}\)
\(\sin x = \frac{1}{2}\sqrt{2}\)
\(x = 45^{\circ}\)
Jadi,
\(\tan 45^{\circ} = 1\)
Salah
\(4\sin x \:-\:2\sqrt{2} = 0\)
\(4\sin x = 2\sqrt{2}\)
\(\sin x = \frac{1}{2}\sqrt{2}\)
\(x = 45^{\circ}\)
Jadi,
\(\tan 45^{\circ} = 1\)
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Pertanyaan 28 dari 30
28. Pertanyaan
1 pointsPerhatikan gambar berikut:
Nilai \(\sin \alpha = \dotso\)
Benar
Panjang sisi miring = \(\sqrt{15^2 + 8^2}\)
Panjang sisi miring = \(\sqrt{225 + 64}\)
Panjang sisi miring = \(\sqrt{289} = 17\)
\(\sin \alpha = \dfrac{\text{depan}}{\text{miring}}\)
\(\sin \alpha = -\dfrac{8}{17}\)
Di kuadran IV nilai \(\sin \alpha\) negatif
Salah
Panjang sisi miring = \(\sqrt{15^2 + 8^2}\)
Panjang sisi miring = \(\sqrt{225 + 64}\)
Panjang sisi miring = \(\sqrt{289} = 17\)
\(\sin \alpha = \dfrac{\text{depan}}{\text{miring}}\)
\(\sin \alpha = -\dfrac{8}{17}\)
Di kuadran IV nilai \(\sin \alpha\) negatif
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Pertanyaan 29 dari 30
29. Pertanyaan
1 pointsPerhatikan gambar berikut:
Nilai \(\cot \beta = \dotso\)
Benar
\(\cot \beta = \dfrac{\text{samping}}{\text{depan}}\)
\(\cot \beta = \dfrac{24}{7}\)
Di kuadran III nilai \(\cot \beta\) positif
Salah
\(\cot \beta = \dfrac{\text{samping}}{\text{depan}}\)
\(\cot \beta = \dfrac{24}{7}\)
Di kuadran III nilai \(\cot \beta\) positif
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Pertanyaan 30 dari 30
30. Pertanyaan
1 pointsPerhatikan gambar berikut:
Nilai \(\cos \gamma = \dotso\)
Benar
Panjang sisi miring = \(\sqrt{6^2 + 8^2}\)
Panjang sisi miring = \(\sqrt{36 + 64}\)
Panjang sisi miring = \(\sqrt{100} = 10\)
\(\cos \gamma = \dfrac{\text{samping}}{\text{miring}}\)
\(\cos \gamma = -\dfrac{8}{10}\)
\(\cos \gamma = -0,8\)
Di kuadran II \(\cos \gamma\) bernilai negatif
Salah
Panjang sisi miring = \(\sqrt{6^2 + 8^2}\)
Panjang sisi miring = \(\sqrt{36 + 64}\)
Panjang sisi miring = \(\sqrt{100} = 10\)
\(\cos \gamma = \dfrac{\text{samping}}{\text{miring}}\)
\(\cos \gamma = -\dfrac{8}{10}\)
\(\cos \gamma = -0,8\)
Di kuadran II \(\cos \gamma\) bernilai negatif