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Home Question Bank Math Trigonometry Archive 2024 November 28

Trigonometry Questions from Nov 28,2024

Browse the Trigonometry Q&A Archive for Nov 28,2024, featuring a collection of homework questions and answers from this day. Find detailed solutions to enhance your understanding.

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276. Найдите значение \( \sin \alpha, \cos \alpha, \operatorname{tg} \alpha, \operatorname{ctg} \alpha, \sec \alpha \) и \( \operatorname{cosec} \alpha \) для угла \( \alpha=-45^{\circ} \). 1. Simplifique: \( E=(\operatorname{Sen} x+\operatorname{Cos} x)^{2}+(\operatorname{Sen} x-\operatorname{Cos} x)^{2} \) 272. Найдите аначение выражсния \( \sin \alpha+\cos \alpha-\operatorname{tg} \alpha \), если \( \sin \alpha=0,6 \). Единствнное ли это решение? 27. Escriban el cálculo y resuelvan. a. El doble del complemento de \( 34^{\circ} 25^{\prime} \) más la tercera parte de \( 158^{\circ} \). Si tg \( \alpha=\frac{5}{12}, y \alpha \) es un ángulo agudo, calcula sin obtener el ángulo \( \alpha \), a) \( \cos \alpha, \operatorname{sen} \alpha, \sec \alpha y \operatorname{cosec} \alpha \) Si \( \operatorname{tg} \alpha=\frac{5}{12} \), y \( \alpha \) es un ángulo agudo, calcula sin obtener el ángulo \( \alpha \), a) \( \cos \alpha \), sen \( \alpha \), sec \( \alpha \) y cosec \( \alpha \) b) Las razones trigonométricas (seno, coseno y tangente) del ángulo complementario de \( \alpha \) (1,5 puntos) (a) Given that \( \sin ^{-1} x=A \) and \( \cos ^{-1} x=B \) where \( A, B \) are acute angles show that \( \sin ^{-1} x+\cos ^{-1} x=\frac{\pi}{2} \) (b) Hence solve the equation \( \cos ^{-1} x-\sin ^{-1} x=\frac{\pi}{3} \). 34. Find one single formula for the general solution of the equation \( 5 \cos 2 \theta+8 \sin ^{4} \theta-3=0 \) and a particular solution for which \( \frac{7 \pi}{2}<\theta<4 \pi \). 35. Given that \( \tan \alpha=\frac{r \sin \theta}{1-r \cos \theta} \). \( \sin \theta \neq 0 \) and that \( \alpha=\pi-2 \theta \). prove that \( r=2 \sin \frac{1}{2} \alpha \) Si: \( \operatorname{Sen} x . \operatorname{Cos} x=1,5 \), halle: \( P=\operatorname{Sen} x+\operatorname{Cos} x \) Simplifique: \( \quad M=\sqrt{1+2 \operatorname{Sen} \alpha \cdot \operatorname{Cos} \alpha}-\operatorname{Sen} \alpha \)
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