Trigonometry Questions from Nov 23,2024

Browse the Trigonometry Q&A Archive for Nov 23,2024, featuring a collection of homework questions and answers from this day. Find detailed solutions to enhance your understanding.

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Given that \( 7 \cot ^{2} x-5 \operatorname{cosec}^{2} x=2 \), and that \( x \) is obtuse, find the exact value of \( \cos x \) b) \( 2 \tan ^{2} \alpha+3 \sec \alpha=0 \) b) \( 2 \tan ^{2} \alpha+3 \sec \alpha=0 \) IVEL: BASICO Encuentra el valor de " \( x \) " en los siguientes casos: ) \( \cos \left(x+20^{\circ}\right) \csc \left(80^{\circ}-2 x\right)=1 \) ) \( \tan \left(8 x-40^{\circ}\right) \sec \left(5 x+7^{\circ}\right)=1 \) cot \( \left(3 x+60^{\circ}\right)=1 \) a) \( 4 \operatorname{sen}^{2} \alpha+4 \operatorname{sen} \alpha=3 \) 1. Найдите область определения функции \( y=V \cos (x) \). \( \begin{array}{ll}\text { a) } x \in R \quad ; \text { б) } x \geq 0 & \text { в) } 2 \pi \cdot n \leq x \leq \pi+2 \pi \cdot n, n \in Z \\ \text { г) }-\frac{\pi}{2}+2 \pi \cdot n \leq x \leq \frac{\pi}{2}+2 \pi \cdot n, n \in Z\end{array} \) 8.-un aeroplano P de la fuerza aérea, que vuela a 3000 m sobre un punto R que esta en la superficie del agua, localiza a un submarino S a nivel del agua y un ángulo de depresión de \( 37^{\circ} \), asi como un buque destructor T a un ángulo de depresión de \( 21^{\circ} \) además, el ángulo SPT resulta ser de \( 110^{\circ} \) calcula la distancia entre en submarino y el buque destructor. Exercicể: Vérifiez que : \( \sqrt{3+2 \sqrt{2}}=1+\sqrt{2} \). 1. a. Résolvez dans \( \mathbb{R} \) l'équation : \( \quad 2 x^{2}+(1-\sqrt{2}) x-\frac{\sqrt{2}}{2}=0 \) b. Résolvez dans \( \mathbb{R} \) l'inéquation : \( 2 x^{2}+(1-\sqrt{2}) x-\frac{\sqrt{2}}{2} \leq 0 \) 2. Déduisez de la question 1\( ) \) a) la résolution de l'équation : \( 2 \cos ^{2}(x)+(1-\sqrt{2}) \cos (x)-\frac{\sqrt{2}}{2}=0 \). Représentez sur le cercle trigonométrique, les images des solutions de l'équation précédente. 3. Déduisez de la question 1\( ) \) b) les solutions dans \( [0 ; 2 \pi] \) de l'inéquation: \( 2 \cos ^{2}(x)+(1-\sqrt{2}) \cos (x)-\frac{\sqrt{2}}{2} \leq 0 \). Représentez sur le cercle trigonométrique, les images des solutions de l'inéquation précédente. Choose all of the equations below that have only one solution for \( x \) when \[ 0^{\circ} \leq x \leq 360^{\circ} \] \[ \begin{array}{llll}\sin x=-1 & \sin x=0 & \sin x=0.5 & \sin x=1 \\ \cos x=-1 & \cos x=0 & \cos x=0.5 & \cos x=1\end{array} \] 7. A bdder of length 6 m bass against a wall. The foot of the bodder is at a distance of 3 m from the base of the wall. Calculate the angle between the ladder and the ground.
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