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Home Question Bank Math Trigonometry Archive 2025 January 18

Trigonometry Questions from Jan 18,2025

Browse the Trigonometry Q&A Archive for Jan 18,2025, featuring a collection of homework questions and answers from this day. Find detailed solutions to enhance your understanding.

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Calcule \( Q=\frac{\tan ^{4} 60^{\circ}-\sec ^{4} 45^{\circ}}{\left(\sec 30^{\circ}-\cot 60^{\circ}\right)^{2}} \) Uma escada de 5 metros está encostada em uma parede, formando um ângulo de elevação com o solo. Calcule a altura que a escada atinge na parede utilizando funções trigonométricas inversas. Ejercicio 003 Encontrar el ángulo de desfase entre las senoides \( V_{1}=-10 \cos \left(w t+50^{\circ}\right) \) y \( V_{2}=12 \sin \left(w t-10^{\circ}\right) \) e indicar cuál se adelanta. A partir de la identidad pitagórica, deriva la relación entre \( \cot(x) \), \( \sin(x) \) y \( \cos(x) \). 0) \( \operatorname{tg} 2 x+2 \cos x=0 \rightarrow \) Utilize the half-angle identity to determine \( \cos\left(\frac{3\pi}{4}\right) \). [15] If \( \sin 30^{\circ}=\cos \theta \), where \( \theta \) is an acute angle, then \( \mathrm{m}(\angle \theta)= \) \qquad (a) 10 (b) 30 (c) 45 (d) 60 [15] If \( \sin 30^{\circ}=\cos \theta \), where \( \theta \) is an acute angle, then \( \mathrm{m}(\angle \boldsymbol{\theta})= \) \( \qquad \) (a) 10 (b) 30 (c) 45 (d) 60 [16] In \( \triangle \mathrm{ABC} \), if \( \mathrm{m}(\angle B)=\mathbf{9 0}^{\circ} \), then \( \sin A+\cos C= \) \( \qquad \) (a) \( 2 \sin \mathrm{~A} \) (b) \( 2 \sin \mathrm{C} \) (c) \( 2 \sin b \) (d) \( 2 \cos \mathrm{~A} \) [17] The slope of the straight line which is parallel to \( \boldsymbol{x} \)-axis is \( \qquad \) (a) -1 (b) 0 (c) 1 (d) undefined [18] If the origin point is a centre of a circle of radius 3 unit length, then the point \( \qquad \) belongs to it. (a) \( (1,2) \) (b) \( (-2, \sqrt{5}) \) Using the sum formula for cosine, express \( \cos(a + b) \) in terms of \( \cos a, \cos b, \sin a, \text{ and } \sin b \). Derive an expression for \( \sin(a+b) \) using the sum formulas, where \( a = 60^{\circ} \) and \( b = 45^{\circ} \).
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