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Home Question Bank Math Trigonometry Archive 2024 November 19

Trigonometry Questions from Nov 19,2024

Browse the Trigonometry Q&A Archive for Nov 19,2024, featuring a collection of homework questions and answers from this day. Find detailed solutions to enhance your understanding.

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\( \sin ( x + 5 ) + \log x = 3 \cos x , y \) Demostrar la identidad. \[ \cos ^{2} x-\operatorname{sen}^{2} x=1-2 \operatorname{sen}^{2} x \] Observe que cada proposición debe estar basada en una regla seleccionada del menú de reglas. Para ver una descripción detallada de una regla, seleccione el signo de interrogación correspondiente. Proposición \( \cos ^{2} x-\operatorname{sen}^{2} x \) 1. Resuelva \( \sec ^{2} x+\tan ^{2} x=3 \tan x \) \( \begin{array}{lll}\text { A) } 30^{\circ} & \text { B) } 45^{\circ} & \text { C) } 60^{\circ} \\ \text { D) } 75^{\circ} & \text { E) } 82^{\circ} & \end{array} \) La altura respecto al suelo de un objeto que se mueve con movimiento armónico siempre está determinado por la expresión \( \sqrt{2} \operatorname{sen}\left(\frac{\pi t}{3}\right)+\sqrt{2} \cos \left(\frac{\pi t}{3}\right)+3 \quad \) en metros, donde \( 0 \leq t \leq 12 \) es el tiempo en minutos. Determine el tiempo en el cual el objeto se encontró a cuatro metros de altura respecto al suelo por segunda vez. \( \begin{array}{lll}\text { A) } 5,75 \mathrm{~min} & \text { B) } 4,5 \mathrm{~min} & \text { C) } 6,25 \mathrm{~min} \\ \text { D) } 8 \mathrm{~min} & \text { E) } 9 \mathrm{~min} & \end{array} \) 17) Find \( \sin \theta \) and \( \tan \theta \) if \( \cos \theta=\frac{2}{3} \) and \( \cot \theta>0 \) 18) Find \( \tan \theta \) and \( \sec \theta \) if \( \sin \theta=-\frac{2}{5} \) and \( \cos \theta>0 \) 19) Find \( \sec \theta \) and \( \csc \theta \) if \( \cot \theta=-\frac{4}{3} \) and \( \cos \theta<0 \) 20) Find \( \sin \theta \) and \( \cos \theta \) if \( \cot \theta=\frac{3}{8} \) and \( \sec \theta<0 \) Resuelva sen \( 9 x+\operatorname{sen} 5 x+2 \operatorname{sen}^{2} x=1 \) \( \begin{array}{lll}\text { A) } \frac{\pi}{24} & \text { B) } \frac{\pi}{12} & \text { C) } \frac{\pi}{16} \\ \text { D) } \frac{\pi}{42} & \text { E) } \frac{\pi}{15} & \end{array} \) 1. Standing on a cliff 380 m above the sea, Pat sees an approaching ship and measures its angle of depression, obtaing \( 9^{\circ} \). How far from shore is the ship? Now Pat sights a second ship beyond the first. The angle of depression of the second ship is \( 5^{\circ} \). How lar apart are the ships? Solve for the missing parts of the right \( \triangle A B C \). Round sides to the nearest tenth. \( \begin{array}{lll}\text { 11) } A=20^{\circ}, a=18 & \text { 12) } A=58^{\circ}, b=34 & \text { 13) } A=82^{\circ}, c=540\end{array} \) 3) An airplane takes off from 200 yards in front of a 60 ft building. At what angle of elevation must the plane take off to avoid crashing into the building? Assume that the airplane flies in a straight line and the angle of elevation remains constant until the arplane flies over the building. Prove the following trigonometric identity: \( \frac{\sin A\left[1-\sin \left(360^{\circ}-A\right)\right]}{1-\cos ^{2}\left(180^{\circ}+A\right)}-1=\operatorname{cosec} A \)
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