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Home Question Bank Math Trigonometry Archive 2024 December 03

Trigonometry Questions from Dec 03,2024

Browse the Trigonometry Q&A Archive for Dec 03,2024, featuring a collection of homework questions and answers from this day. Find detailed solutions to enhance your understanding.

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\( \frac { 1 - 2 \sin ^ { 2 } ( \pi + \alpha ) } { \sin ( \frac { \pi } { 2 } + \alpha ) + \sin ( \pi - \alpha ) } + \frac { 1 - 2 \cos ^ { 2 } ( \pi - \alpha ) } { \cos ( \pi + \alpha ) + \cos ( \frac { \pi } { 2 } - \alpha ) } \) 1) Sketch one cycle for the following trigonometric function and complete the properties below. \[ y=-2 \sin \left[\frac{1}{4}\left(x+\frac{2 \pi}{3}\right)\right]-5 \] 7 Si sabemos que \( \cos \frac{\alpha}{2}=-\frac{1}{3} \) y que \( 180^{\circ}<\alpha<270^{\circ} \) halla \( \cos 2 \alpha \) sin hallar el ángulo \( \alpha \). Ejercicio: Calcule, si es posible, el valor de \( x \) en las expresiones: 1. \( x \operatorname{cosec} 60^{\circ}-x \operatorname{tg} 45^{\circ}+1=0 \) Halle con máquina de calcular \[ \begin{array}{l}\text { a) } \operatorname{sen} 23^{\circ} 14^{\prime} \\ \text { b) } \cos 10^{\circ} 12^{\prime} \\ \text { c) } \operatorname{tg} \frac{\pi}{6}\end{array} \] 6) Solve the trigonometric equations over the interval \( 0 \leq x \leq 2 \pi \) a) \( 2 \sin 2 x-\sin x=0 \) b) \( \cos 2 x+\sin ^{2} x-4 \cos x+3=0 \) c) \( 2 \csc x^{2}-8=0 \) ( \( 2=0 \) 1) Teniendo en cuenta que \( \forall \alpha \in \mathbf{R}: \operatorname{sen}^{2} \alpha+\cos ^{2} \alpha=1 \) y utilizando la máquina de calcular verifique para el caso \[ \begin{array}{c}\alpha=\frac{\pi}{2}, \alpha-\frac{7}{6} \pi, \alpha=\frac{\pi}{3}+2 k \pi \\ \alpha=-\frac{\pi}{2}, \alpha=-\frac{\pi}{6}\end{array} \] Bapuarr 2 1. a) \( \cos \alpha=-\frac{1}{3}, \pi<\alpha<\frac{3 \pi}{2} \). Haimu \( \sin \alpha, \operatorname{tg} \alpha, \operatorname{ctg} \alpha \) of \( \operatorname{tg} \alpha=4, \alpha-11 / \operatorname{ser} \). Havimu \( \sin \alpha, \cos \alpha, \operatorname{ctg} \alpha \) Solve the following equation on the interval \( [0,2 \pi) \). \[ \begin{array}{l}\tan (3 x)=-\sqrt{3}\end{array} \] A. \( \begin{array}{l}x=\square \\ \text { (Type an exact answer, using } \pi \text { as needed. Use a comma to separate an } \\ \text { your answer. Use integers or fractions for any numbers in the expression } \\ \text { B. There is no solution. }\end{array} \) 1) Sketch one cycle for the following trigonometric function and complete the properties below. \[ y=-2 \sin \left[\frac{1}{4}\left(x+\frac{2 \pi}{3}\right)\right]-5 \]
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