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Home Question Bank Math Trigonometry Archive 2025 January 13

Trigonometry Questions from Jan 13,2025

Browse the Trigonometry Q&A Archive for Jan 13,2025, featuring a collection of homework questions and answers from this day. Find detailed solutions to enhance your understanding.

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(2) Given that \( \sin 35^{\circ}=\boldsymbol{p} \), express each of the following in terms of \( \boldsymbol{p} \) : \( \begin{array}{ll}\text { a) } \cos 325^{\circ} & \text { c) } \cos 70^{\circ} \\ \text { b) } \sin 55^{\circ} & \text { d) } \cos 95^{\circ}\end{array} \) \( [ \sin ( - \theta ) + \cos ( 360 - \theta ) ] [ \cos ( 90 - \theta ) + \frac { \sin \theta } { \tan \theta } ] \) \( \frac{\sin 210^{\circ} \cos 300^{\circ} \tan 240^{\circ}}{\cos 120^{\circ} \tan 150^{\circ} \sin 330^{\circ}} \) \( [\sin (-\theta)+\cos (360-\theta)]\left[\cos (90-\theta)+\frac{\sin \theta}{\tan \theta}\right] \) If \( \quad \tan x=m+\frac{1}{m}, 90^{\circ} \leq x \leq 270^{\circ} \) and \( m^{2}+\frac{1}{m^{2}}=1 \) Calculate the value of \( x \) without the use of a calculator. havión vuela a una altitud de 10.000 m . En un determinado momento, el piloto observa una ci n un ángulo de depresión de \( 30^{\circ} \). A qué distancia horizontal se encuentra el avión de la ciuda UTAS PARA LA SOLUCION: Dibuja un diagrama: imagine una línea horizontal que representa el suelo y otra vertica representa la altitud del avión. El ángulo de depresión es el ángulo que forma la línea de del piloto con la horizontal, hacia abajo Identifique el triángulo rectángulo El thángulo rectángulo se forma por: - La altura del avión (cateto opuesto al ángulo de depresión) - La distancia horizontal del avión a la ciudad (cateto adyacente al ángulo de depre Elija la razón trigonométrica: Como se conoce el cateto opuesto (altura) y se quiere hi cateto adyacente, qué razón se utiliza? Escribala. Plantee la ecuación Resuélvala y dé la respuesta. A right triangle has an angle measuring 60 degrees and its hypotenuse measures 10 cm. Find the measure of the side opposite to the 60-degree angle. \( 6.2[\sin (-\theta)+\cos (360-\theta)]\left[\cos (90-\theta)+\frac{\sin \theta}{\tan \theta}\right] \) 6.3 If \( \tan x=m+\frac{1}{m}, 90^{\circ} \leq x \leq 270^{\circ} \) and \( m^{2}+\frac{1}{m^{2}}=1 \) Calculate the value of \( x \) without the use of a calculator. Simplify the following expressions \( 6.1 \frac{\sin 210^{\circ} \cos 300^{\circ} \tan 240^{\circ}}{\cos 120^{\circ} \tan 150^{\circ} \sin 330^{\circ}} \) If \( \tan x=m+\frac{1}{m}, 90^{\circ} \leq x \leq 270^{\circ} \) and \( m^{2}+\frac{1}{m^{2}}=1 \) Calculate the value of \( x \) without the use of a calculato \( [ \sin ( - \theta ) + \cos ( 360 - \theta ) ] [ \cos ( 90 - \theta ) + \frac { \sin \theta } { \tan \theta } ] . \) \( 6.1 \frac{\sin 210^{\circ} \cos 300^{\circ} \tan 240^{\circ}}{\cos 120^{\circ} \tan 150^{\circ} \sin 330^{\circ}} \) \( 6.2 \quad[\sin (-\theta)+\cos (360-\theta)]\left[\cos (90-\theta)+\frac{\sin \theta}{\tan \theta}\right] \) 6.3 If \( \tan x=m+\frac{1}{m}, 90^{\circ} \leq x \leq 270^{\circ} \) and \( m^{2}+\frac{1}{m^{2}}=1 \) Calculate the value of \( x \) without the use of a calculator.
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