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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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What is the phase shift of the function \( f(x)=\sin \left(x-\frac{\pi}{2}\right) ? \) (1 point) \( \frac{\pi}{\frac{\pi}{2}} \) \( \frac{\pi}{4} \) 1 Which of the following sine functions is equivalent to \( f(x)=\cos (x) \) ? Option \#1: \( f(x)=\sin \left(x-\frac{\pi}{2}\right) \) Option \#2: \( f(x)=\sin \left(x+\frac{\pi}{2}\right) \) Option \#3: \( f(x)=\sin (x+\pi) \) (1 point) Option \# The graph of \( \sin (x+c) \) is shifted \( \frac{3 \pi}{2} \) units to the left compared to \( \sin x \). What is the value of \( c \) ? (1 point) \( c=\square \) The graph of \( \sin (x+c) \) is shifted \( \frac{\pi}{5} \) units to the right compared to \( \sin x \). What is the value of \( c \) ? (1 point) \( c=\square \) Find the area of the triangle if \( A=12.8^{\circ}, b=10.8 \) meters, and \( c=6.4 \) meters. Area \( =\square \mathrm{m}^{2} \) (Round to the nearest tenth as needed.) 8. Um avião está a 1300 m de medida de altura quando começa um movimento dedescida para a pista deaterrissagem, em uma linha imaginária que forma um ângulo de medida de abertura de \( 30^{\circ} \) com o solo. Qual será a medida da distância percorrida pelo aviāo até tocar o o solo? Decide on the suitable procedure to solve the triangle given the following information, then solve the triangle. \( \mathrm{a}=26.21, \mathrm{c}=34.75, \mathrm{C}=15^{\circ} 31^{\prime} \) Which of the following procedures should be used to solve the triangle? A. Use the angle sum formula to find the remaining angle, and the law of sines to find the remaining sides. B. Use the law of sines to find an angle. Then use the angle sum formula to find the remaining angle. Use the law of sines to find the remaining side. C. Use the law of cosines to find the third side and the law of sines to find the smaller of the two remaining angles. Use the angle sum formula to find the last angle. D. Use the law of cosines to find the largest angle. Use the law of sines to find either remaining angle. Use the angle sum formula to find the last angle. Decide on the procedure to solve the triangle given the following information, then solve the triangle. \( \mathrm{a}=51.41, \mathrm{~b}=37.11, \mathrm{c}=66.53 \) Which of the following procedures should be used to solve the triangle? A. Use the law of cosines to find the largest angle. Use the law of sines to find either remaining angle. Use the angle sum formula to find the remaining angle. B. Use the angle sum formula to find the remaining angle and the law of sines to find the remaining sides. C. Use the law of cosines to find the third side and the law of sines to find the smaller of the two remaining angles. Use the angle sum formula find the remaining angle. D. Use the law of sines to find an angle. Then use the angle sum formula to find the remaining angle. Use the law of sines to find the remaining side. 7. A pipa de Joaquim ficou presa em uma árvore. A linha da pipa ficou esticada, formando com o chāo um ângulo de medida de abertura de \( 45^{\circ} \). O comprimento da linha da pipa mede 8,5 m. Determine a medida da altura da pipa em relaçāo ao solo. (Utilize: \( \sqrt{2}=1,4 \) ). 18. Find the exact value in radians of each of the expressions below: (3 points each) \begin{tabular}{|l|l|l|}\hline a. \( \arcsin \left(-\frac{1}{\sqrt{2}}\right)= \) & b. \( \cos ^{-1}\left(-\frac{1}{2}\right)= \) & c. \( \tan ^{-1}\left(\frac{1}{\sqrt{3}}\right)= \) \\ \hline\end{tabular}
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