Question
Download Solution PDF\(\sin \frac{{21\pi }}{2}\) और cos(-1740°) का मान ज्ञात कीजिये?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFसंकल्पना:
cos (-θ) = cos θ
cos (2nπ - θ) = cos θ
| डिग्री में कोण | 0° | 30° | 45° | 60° | 90° |
| sin | 0 | 1/2 | \(1/\sqrt2\) | \(\sqrt3/2\) | 1 |
| cos | 1 | \(\sqrt3/2\) | \(1/\sqrt2\) | 1/2 | 0 |
| tan | 0 | \(1/\sqrt3\) | 1 | \(\sqrt3\) | अपरिभाषित |
गणना:
हमारे पास है,
⇒ \(sin(\frac{21π}{2})\)
जब तक कोण 0 और 2π के बीच न हो जाए, तब तक 2π का पूरा घुमाव हटा दें।
⇒ \(sin(\frac{21π}{2})= sin(5\times 2\pi +\frac{π}{2}) =sin(\frac{π}{2})\)
जैसा कि हम जानते हैं कि \(sin(\frac{π}{2})\) का मान 1 है
जैसा कि हम जानते हैं, cos θ का मान 2π या 360° के अंतराल के बाद दोहराता है।
⇒ cos (-1740°) = cos (1740°) [∵ cos (-θ) = cos θ]
हम जानते हैं कि cos (2nπ - θ) = cos θ
चूँकि sin θ और cos θ का आवर्तकाल 360° है।
⇒ cos (1740°) = cos (5 × 360° - 1740°)
⇒ cos (1740°) = cos (1800° - 1740°)
⇒ cos (1740°) = cos (60°)
हम जानते हैं कि, cos 60° = 1/2
⇒ cos (-1740°) = 1/2.
∴ \(\sin \frac{{21\pi }}{2}\) का मान 1 है और cos (-1740°) का मान 1/2 है।
Last updated on May 26, 2025
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