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Home Question Bank Math Trigonometry Archive 2024 December 19

Trigonometry Questions from Dec 19,2024

Browse the Trigonometry Q&A Archive for Dec 19,2024, featuring a collection of homework questions and answers from this day. Find detailed solutions to enhance your understanding.

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If the hypotenuse of a right triangle measures 10 units and the length of the opposite side is 6 units, what is the value of the cosecant of the angle opposite the 6-unit side? 1. State whether each of the following are true or false. For those that are false, justify your decision. a) \( \cos (\theta+2 \pi)=\cos \theta \) b) \( \sin (\pi-\theta)=-\sin \theta \) c) \( \cos \theta=-\cos (\theta+4 \pi) \) Graph the trigonometric function. \[ y=3 \cos \left(x+\frac{2 \pi}{3}\right) \] Plot all points corresponding to \( x \)-intercepts, minima, and maxima within one cycle Right triangle \( A B C \) has its right angle at \( C \). \[ \begin{array}{l}A C=12 \text { and } B C=5 \text {. } \\ \text { Which trigonometric ratios are correct? } \\ \text { Select each correct answer. } \\ \square \sin B=\frac{12}{13} \\ \tan B=\frac{5}{12} \\ \square \sin A=\frac{5}{13} \\ \square \cos A=\frac{12}{13} \\ \tan A=\frac{12}{13}\end{array} \] 3. Si en el triángulo \( \mathrm{ABC}, \operatorname{sen} A=\frac{1}{5} \) determina la medida de los lados de triángulo Simplify the expression by using a double-angle formula. \[ 2 \cos ^{2} \frac{\pi}{7}-1 \] Let \( \theta \) be an angle in quadrant II such that \( \cos \theta=-\frac{4}{7} \). Find the exact values of \( \csc \theta \) and \( \tan \theta \). Find the exact value of \[ \sin \left[\tan ^{-1}(-1)+3 \cos ^{-1}\left(-\frac{1}{2}\right)\right] \] Find the exact value of \( \sin ^{-1}\left(-\frac{\sqrt{3}}{2}\right) \) Write your answer in radians in terms of \( \pi \). Find all solutions of the equation in the interval \( [0,2 \pi) \) \[ 2 \cos \theta-\sqrt{3}=0 \] Write your answer in radians in terms of \( \pi \). .If there is more than one solution, separate them with commas.
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