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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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Série Exercicex \( 1 / \) Montrer que pour tout réel \( x \) on a \( \sqrt{2} \sin \left(x+\frac{3 \pi}{4}\right)=\cos x-\sin x \) \( 2 / \) Soit \( f(x)=\cos 2 x-\sin 2 x+1 \) a/Calculer \( f\left(\frac{\pi}{12}\right) \) b/Vérifier que \( f(x)=2 \sqrt{2} \cos x \sin \left(x+\frac{3 \pi}{4}\right) \) c/Déduire \( \cos \left(\frac{\pi}{12}\right) \) \( 3 / \) a/Montrer que pour tout réel \( x \) de \( ] 0, \frac{\pi}{4}\left[\right. \) on \( a: \quad \frac{2 \cos 2 x}{\cos 2 x-\sin 2 x+1}=1+\tan x \) b/En déduire que tan \( \left(\frac{\pi}{12}\right)=2-\sqrt{3} \) ts) Convert \( 4 \cos ^{2} \theta+9 \sin ^{2} \theta=\frac{36}{r^{2}} \) into a rectangular equation. Show all work for full credit. 16. Use the identity for \( \sin (x-y) \) to show that sine is an odd function (i.e., \( \sin (-x)=-\sin (x)) \). Hint: let \( x=0^{\circ} \). If the value of \( \cos \theta=-\frac{\sqrt{3}}{2} \), which of the following could be true? ont le même point image sur un cercle trigonomé- trique. \( \begin{array}{llll}\cdot \frac{\pi}{3} & \cdot 0 & \cdot-\frac{5 \pi}{3} & \cdot \pi \\ \cdot \frac{19 \pi}{4} & \cdot-\frac{23 \pi}{6} & \cdot \frac{7 \pi}{3} & \cdot-\frac{3 \pi}{4} \\ \cdot-8 \pi & \cdot \frac{\pi}{6} & \cdot \frac{13 \pi}{4} & \cdot-\frac{19 \pi}{4} \\ & & \end{array} \) \( -\frac{\pi}{2}<\theta \leq \frac{\pi}{2} \). Find the value of \( \theta \) in radians. \( \cot (\theta)=0 \) Write your answer in simplified, rationalized form. Do not round. \( \theta=\square \) What is the period of the function \( f(x)=2-\sin \left(\frac{1}{2} x\right) \) ? \( -90^{\circ} \leq \theta \leq 90^{\circ} \). Find the value of \( \theta \) in degrees. \( \csc (\theta)=\frac{2 \sqrt{3}}{3} \) \( \theta= \) Submit 2. \( x=\frac{\operatorname{sen} 30^{\circ}+\frac{1}{2}}{\operatorname{tg} 30^{\circ}-\cot 50^{\circ}} \) \( \frac { 1 + 2 \sin ^ { 2 } \alpha } { \cos \alpha + \sin \alpha } + \frac { 1 - 2 \cos ^ { 2 } \alpha } { - \cos \alpha + \sin \alpha } \)
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