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Home Question Bank Math Trigonometry Archive 2024 December 22

Trigonometry Questions from Dec 22,2024

Browse the Trigonometry Q&A Archive for Dec 22,2024, featuring a collection of homework questions and answers from this day. Find detailed solutions to enhance your understanding.

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If \( \sec (3 \theta+15)=\csc (35-\theta) \) where \( \theta \) is an acute angle, then \( \csc \frac{3}{2} \theta=\cdots \) \( \begin{array}{llll}\text { (a) } 2 & \text { (b) } \sqrt{3} & \text { (c) } \sqrt{2} & \text { (d) } \frac{1}{2}\end{array} \) 11) The measure of the smallest positive angle satisfy the relation : \( 2 \sin \theta=-1 \) is \( \begin{array}{lll}\text { (a) } 30^{\circ} & \text { (b) } 120^{\circ} & \text { (c) } 210^{\circ} y=x\end{array} \) The value of \( \sec \left(300^{\circ}\right) \sin \left(270^{\circ}-\theta\right)+\tan \left(-45^{\circ}\right) \cos \left(360^{\circ}-\theta\right) \) is \( \begin{array}{llll}\text { (a) }-3 \sin \theta & \text { (b) }-3 \cos \theta & \text { (c) } 3 \cos \theta & \text { (d) } 0\end{array} \) (6) The value of \( \sec \left(300^{\circ}\right) \sin \left(270^{\circ}-\theta\right)+\tan \left(-45^{\circ}\right) \cos (3 M-9) \) is \( \begin{array}{lll}\text { (a) }-3 \sin \theta & \text { (b) }-3 \cos \theta & \text { (c) } 3 \cos \theta\end{array} \) (7) If the product of two roots of the equation : \( (k-2) x^{2}-6 x+12=0 \) equals 3 \( \log ( \cos \theta ) + \log ( \sec \theta ) = \ldots \ldots \ldots . . , \theta \in [ 0 , \frac { \pi } { 2 } ] \) 3. Выразите в градусной мере величины углов: а) \( 3 ; \) б) \( -\frac{\pi}{9} \); в) \( \frac{5 \pi}{12} \); г) \( \frac{7 \pi}{3} \); д) 4,2 ; е) \( \frac{\pi}{5} \); ж) \( 0,6 \pi \); з) \( \frac{25}{18} \pi \). If \( \csc \theta=\frac{x+1}{x}, x>0 \), then \( \cot \theta= \) Exercice 1: D. Ecrirc sous forme trigonométrique : \( z_{1}=2\left(\cos \frac{\pi}{4}-i \sin \frac{\pi}{4}\right) \) \( \begin{array}{ll}z_{2}=-3\left(\cos \frac{2 \pi}{3}+i \sin \frac{2 \pi}{3}\right) \quad z_{3}=2\left(\cos \frac{\pi}{4}+i \sin \frac{3 \pi}{4}\right) \\ z_{4}=\cos \frac{\pi}{6}+i \sin \left(-\frac{\pi}{6}\right) \quad z_{5}=\cos \theta-i \sin \theta \quad z_{5}=\sin \theta+i \cos \theta\end{array} \) If \( x \) is in the third quadrant, then \( \cot x \) in terms of \( \sec x \) is A) \( \frac{\sqrt{\sec ^{2} x-1}}{\sec ^{2} x-1} \) B) \( -\frac{\sqrt{\sec ^{2} x-1}}{\sec ^{2} x-1} \) C) \( -\frac{\sqrt{\sec ^{2} x+1}}{\sec ^{2} x-1} \) What is the definition of the cosine function in relation to a right triangle using the adjacent side and hypotenuse?
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