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Home Question Bank Math Trigonometry Archive 2024 November 14

Trigonometry Questions from Nov 14,2024

Browse the Trigonometry Q&A Archive for Nov 14,2024, featuring a collection of homework questions and answers from this day. Find detailed solutions to enhance your understanding.

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Sean \( S, C \) y R las medidas en grados sexagesimales, centesimales y radianes de un mismo ángulo, respectivamente. Se cumple que \( (S / 3-C / 5)^{2}-20 R / \pi>0 \). Calcule el menor valor posible (en radianes) para dicho ángulo positivo, sabiendo que \( S \) y C son números enteros. Q1. Solve the following equations on the interval \( [0,2 \pi) \). \( \begin{array}{ll}\text { a. } 2 \cos x=1 & \text { b. } \sin (2 x)=\cos (x) \\ \text { Hint: } \operatorname{Recall} \sin (2 x)=2 \sin (x) \cos (x)\end{array} \) \( \begin{array}{ll}\text { c. } \csc ^{2}(x)-4=0 & \text { d. } 2(\tan (x)+3)=5+\tan (x)\end{array} \) \( \frac{a}{\operatorname{sen} a}=\frac{b}{\operatorname{sen} \beta}=\frac{c}{\operatorname{sen} \theta} \) La siguiente expresión matemática represent a la a. Ley de cosenos b. Ley de trigonometría c. Ley de senos Simplifique la expresión considerando \( \arctan (a) \neq 0 \) \( H=\frac{\operatorname{arcsen}\left(\frac{2 a}{1+a^{2}}\right)+2 \arccos \left(\frac{1-a^{2}}{1+a^{2}}\right)}{\arctan [\operatorname{arccot}(\tan (2 a))-\operatorname{arccot}(\tan (3 a))]} \) Tu respuesta Calcule el mayor valor de \( x<360^{\circ}, \quad \) * correspondiente al máximo valor de: V=sen \( (4 x)+\cos (4 x) \). Nota: dar el resultado en grados. Tu respuesta It is given that \( \sin x \sin y=\frac{1}{12} \) and \( \cos x \cos y=\frac{3}{4} \) (i) Find the value of \( \cos (x+y) \) and of \( \cos (x-y) \) (ii) Hence, find the acute angles \( x \) and \( y \). Simplifique la expresión considerando \( \arctan (\mathrm{a}) \neq 0 \). \( \mathrm{H}=\frac{\operatorname{arcsen}\left(\frac{2 \mathrm{a}}{1+\mathrm{a}^{2}}\right)+2 \arccos \left(\frac{1-\mathrm{a}^{2}}{1+\mathrm{a}^{2}}\right)}{\arctan [\operatorname{arccot}(\tan (2 \mathrm{a}))-\operatorname{arccot}(\tan (3 \mathrm{a}))]} \) Si \( \operatorname{tg}(x)+\operatorname{ctg}(x)=5 / 2 M= \) \( [\operatorname{sen}(45+x)] /[\operatorname{sen}(135+x)] \) calcule \( M^{2} \) 59. \( y=\cos (2 x-1) \cdot \tan (1-2 x) \) \( \sin x - \cos ( - x ) = \frac { \sqrt { 2 } } { 2 } \)
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