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Home Question Bank Math Trigonometry Archive 2024 November 06

Trigonometry Questions from Nov 06,2024

Browse the Trigonometry Q&A Archive for Nov 06,2024, featuring a collection of homework questions and answers from this day. Find detailed solutions to enhance your understanding.

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4. La expresión correcta para calcular sen \( 225^{\circ} \) sin usar calcualadora es: \( \begin{array}{llll}\text { A. } \operatorname{sen} 180^{\circ}+\operatorname{sen} 45^{\circ} & \text { B. } \operatorname{sen} 200^{\circ}+\operatorname{sen} 25^{\circ} & \text { C. } \operatorname{sen}\left(270^{\circ}-45^{\circ}\right) & \text { D. } \operatorname{sen}\left(180^{\circ}-45^{\circ}\right)\end{array} \) (10) Dos personas están separadas 2 km de distancia. Sobre su plano vertical y en el mismo momento, hay una nube bajo ángulos respectivos de \( 73^{\circ} \) y \( 84^{\circ} \). Calcula la altura de la nube y la distancia de la mis- ma a cada una de las personas. 10. \( \frac{1+\operatorname{Sen} A}{\operatorname{Cos} A}+\frac{\operatorname{Cos} A}{\operatorname{Sen} A}=\frac{1+\operatorname{Sen} A}{\operatorname{Sen} A \cdot \operatorname{Cos} A} \) 12. \( \frac{1-\operatorname{Cos} A}{\operatorname{Sen} A}+\frac{\operatorname{Sen} A}{1-\operatorname{Cos} A}=2 \operatorname{Cec} A \) 14. \( \frac{1}{1-\operatorname{Sen} B}=\operatorname{Sec}^{2} B+\operatorname{Sec} B \operatorname{Tan} B \) 16. \( \operatorname{Tan}^{2} B-\operatorname{Sen}^{2} B=\operatorname{Tan}^{2} B \operatorname{Sen}^{2} B \) 18. \( \frac{\operatorname{Sen} \theta-\operatorname{Sen}^{3} \theta}{\operatorname{Cos}^{2} \theta}=\frac{1}{\operatorname{Csc} \theta} \) 20. \( \frac{\operatorname{Cos}^{4} \alpha-\operatorname{Sen}^{4} \alpha}{1-\operatorname{Tan}^{4} \alpha}=\operatorname{Cos}^{4} \alpha \) 1. For each trigonometric ratio, use a sketch to determine in which quadrant the terminal arm of the principal angle lies, the value of the related acute angle, and the sign of the ratio. \( \begin{array}{ll}\text { a) } \sin \frac{3 \pi}{4} & \text { d) } \sec \frac{5 \pi}{6} \\ \text { b) } \cos \frac{5 \pi}{3} & \text { e) } \cos \frac{2 \pi}{3} \\ \text { c) } \tan \frac{4 \pi}{3} & \text { f) } \cot \frac{7 \pi}{4}\end{array} \) 9. \( \frac{\operatorname{Tan}^{2} \theta+1}{\operatorname{Tan}^{2} \theta}=\operatorname{Csc}^{2} \theta \) 11. \( \frac{\operatorname{Tan} A}{\operatorname{Sec} A}-\frac{\operatorname{Sec} A-\operatorname{Cos} A}{\operatorname{Tan} A}=0 \) 13. \( \frac{\operatorname{Sen} A}{1+\operatorname{Sec} A}-\frac{\operatorname{Sen} A}{1-\operatorname{Sec} A}=2 \operatorname{Cot} A \) 15. \( \operatorname{Sec}{ }^{2} B-\operatorname{Csc}{ }^{2} B=\frac{\operatorname{Tan} B-\operatorname{Cot} B}{\operatorname{Sen} B \operatorname{Cos} B} \) 17. \( \frac{1}{1+\operatorname{Sen} x}=\frac{1-\operatorname{Sen} x}{\operatorname{Cos}^{2} x} \) 19. \( \frac{\operatorname{Sec} \alpha+1}{\operatorname{Sen} \alpha}=\frac{\operatorname{Tan} \alpha}{\operatorname{Cos} \alpha(\operatorname{Sec} \alpha-1)} \) La expresión para calcular tan \( 150^{\circ} \) usando identidades de suma y diferencia de ángulos sin usar calculadora es: \( \begin{array}{llll}\tan \left(100^{\circ}+50^{\circ}\right) & \text { B. } \tan \left(30^{\circ}+120^{\circ}\right) & \text { C. } 2 \tan 75^{\circ} & \text { D. } \tan \left(60^{\circ}+90^{\circ}\right)\end{array} \) 1. Halla, en cada caso, el valor de las funciones trigo- nométricas a partir de \( P(x, y) \). \( \begin{array}{ll}\text { a. }\left(\frac{1}{2},-\frac{\sqrt{3}}{2}\right) & \text { b. }\left(\frac{\sqrt{3}}{2},-\frac{1}{2}\right) \\ \text { c. }\left(\frac{2}{3},-\frac{\sqrt{5}}{3}\right) & \text { d. }\left(\frac{3}{5}, \frac{4}{5}\right)\end{array} \) Solve the following triangle. \( B=30^{\circ}, C=40^{\circ}, b=7 \) A \( \approx \square^{\circ} \) (Simplify your answer.) \( a \approx \square \) \( ( \) Type an integer or decimal rounded to two decimal places as needed.) \( C \approx \square \) (Type an integer or decimal rounded to two decimal places as needed.) 9. Halla sent \( y \) tant, si \( \cos t=-\frac{2}{3} \) y \( t \) se ubica en el segundo cuadrante. \( \sec ^ { 2 } x ( 2 \sin ^ { 2 } x + \cos ^ { 2 } x ) \equiv \sec ^ { 4 } x - \tan ^ { 4 } x \)
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