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Home Question Bank Math Trigonometry Archive 2025 January 02

Trigonometry Questions from Jan 02,2025

Browse the Trigonometry Q&A Archive for Jan 02,2025, featuring a collection of homework questions and answers from this day. Find detailed solutions to enhance your understanding.

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para concluir runlica con tus palabras: ¿por qué se cumple \( \operatorname{sen}\left(40^{\circ}\right)=\cos \left(50^{\circ}\right) \) ? Justifi 43. Evaluate \( \sin \frac{7 \pi}{12} \) as \( \sin \left(\frac{\pi}{4}+\frac{\pi}{3}\right) \) Using the Addition Formulas Use the addition formulas to derive the identities 34. \( \sin \left(x-\frac{\pi}{2}\right)=-\cos x \) one of \( \sin x, \cos x \), and \( \tan x \) is given. Find the other two if \( x \) lies in the specified interval. 8. \( \tan x=2, \quad x \in\left[0, \frac{\pi}{2}\right] \) one of \( \sin x, \cos x \), and \( \tan x \) is given. Find the other two if \( x \) lies in the specified interval. 8. \( \tan x=2, \quad x \in\left[0, \frac{\pi}{2}\right] \) \( \left. \begin{array} { l } { \cos 120 ^ { \circ } \tan 150 ^ { \circ } \sin 330 ^ { \circ } } \\ { [ \sin ( - \theta ) + \cos ( 360 - \theta ) ] [ \cos ( 90 - \theta ) + \frac { \sin \theta } { \tan \theta } ] } \end{array} \right. \) \( 6.1 \frac{\sin 210^{\circ} \cos 300^{\circ} \tan 240^{\circ}}{\cos 120^{\circ} \tan 150^{\circ} \sin 330^{\circ}} \) \( 62[\sin (-\theta)+\cos (360-\theta)]\left[\cos (90-\theta)+\frac{\sin \theta}{\tan \theta}\right] \) 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 calcula What is the definition of the tangent function in relation to a right triangle? Prove that: \( 6.1 \frac{\sin 3 x}{\sin x}-\frac{\cos 3 x}{\cos x}=2 \) \( 6.2 \frac{\cos 3 x}{\sin x}+\frac{\sin 3 x}{\cos x}=\frac{(\cos x+\sin x)(\cos x-\sin x)}{\sin x \cos x} \) \( 6.1 \frac{\sin 210^{\circ} \cos 300^{\circ} \tan 240^{\circ}}{\cos 120^{\circ} \tan 150^{\circ} \sin 330^{\circ}} \) \( 6.2[\sin (-\theta)+\cos (360-\theta)]\left[\cos (90-\theta)+\frac{\sin \theta}{\tan \theta}\right] \) 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. C
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