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Home Question Bank Math Trigonometry Archive 2024 November 21

Trigonometry Questions from Nov 21,2024

Browse the Trigonometry Q&A Archive for Nov 21,2024, 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 period of \( y=\sin (3 x) \) ? \( \begin{array}{l}\frac{\pi}{3} \\ \frac{2 \pi}{3} \\ 3 \pi \\ 6 \pi\end{array} \) What is the general equation of a cosine function with an amplitude of 3 , a period of \( 4 \pi \), and a horizontal shift of \( -\pi \) ? \( \begin{array}{l}y=4 \pi \cos (3(x-\pi)) \\ y=3 \cos (4 \pi(x+\pi)) \\ y=3 \cos (0.5(x+\pi)) \\ y=4 \pi \cos (0.2(x+\pi))\end{array} \) Which transformations are needed to change the parent cosine function to \( y=3 \cos (10(x-\pi)) \) ? vertical compression of 3 , horizontal stretch to a period of \( 5 \pi \), phase shift of \( \pi \) units to the left vertical stretch of 3 , horizontal compression to a period of \( \frac{\pi}{5} \), phase shift of \( \pi \) units to the right vertical compression of 3 , horizontal stretch to a period of 10 p, phase shift of \( \pi \) units to the right vertrech of 3 , horizontal compression to a period of \( \frac{\pi}{5} \), phase shift of \( \pi \) units to the left What is the general equation of a sine function with an amplitude of 2 , a period of \( \pi \) and a horizontal shift of \( \pi \) units \( y=2 \sin (2(x-\pi)) \) \( y=2 \sin (4(x+\pi)) \) \( y=\sin (0.5(x-\pi)) \) \( y=\sin (2(x+\pi)) \) The graph of \( y=\cos \left(x+\frac{\pi}{2}\right) \) is the graph of the \( y=\cos (x) \) shifted in which direction? \( \frac{\pi}{2} \) units to the left \( \frac{\pi}{2} \) units to the right \( \frac{\pi}{2} \) units up \( \frac{\pi}{2} \) units down Which of the following is the graph of \( y=\sin (0.5 x) \) ? Which function has the given properties below? The domain is the set of all real numbers. One \( x \)-intercept is \( \left(\frac{\pi}{2}, 0\right) \). The maximum value is 3 . The \( y \)-intercept is \( (0,-3) \). \( \begin{array}{l}y=-3 \sin (x) \\ y=-3 \cos (x) \\ y=3 \sin (x) \\ y=3 \cos (x)\end{array} \) Which function has the given properties below? The domain is the set of all real numbers. One \( x \)-intercept is \( (2 \pi, 0) \). The amplitude is 4 . The point \( \left(\frac{\pi}{2},-4\right) \) is on the graph. The \( y \)-intercept is \( (0,0) \). \( y=-4 \sin (x) \) \( y=-4 \cos (x) \) \( y=4 \sin (x) \) \( y=4 \cos (x) \) What is the domain of \( f(x)=\cos (x) \) ? the set of real numbers \( -2 \pi \leq x \leq 2 \pi \) the set of real numbers \( -1 \leq x \leq 1 \) the set of real numbers \( 0 \leq x \leq 2 \pi \) the set of all real numbers Which formula gives the \( x \)-coordinates of the maximum values for \( y=\cos (x) \) ? \( k \pi \) for any integer \( k \) \( k \pi \) for \( k=0, \pm 2, \pm 4, \ldots \) \( \frac{k \pi}{2} \) for any positive integer \( k \) \( \frac{k \pi}{2} \) for \( k=0, \pm 2, \pm 4, \ldots \)
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