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Identify the amplitude, period, and phase shift, and graph the function. \[ y=-2 \sin \left(\frac{1}{4} x+\frac{\pi}{8}\right) \]
Trigonometry Jun 06, 2023
Write the given algebraic expression as a function of \( \theta \), where \( 0<\theta<\frac{\pi}{2} \), by making the given substitution. \( \sqrt{81-(x-1)^{2}} ; \) Substitute \( x=9 \sin \theta+1 \)
Pre Calculus Jun 06, 2023
Identify the amplitude of the function. \[ y=-5 \sin x \] 1 \( -5 \) \( \frac{1}{5} \) 5
Trigonometry Jun 06, 2023
Solve the equation over the interval \( [0,2 \pi) \). \[ \tan x=-\frac{\sqrt{3}}{3} \] \( \left\{\frac{\pi}{6}, \frac{7 \pi}{6}\right\} \) \( \left\{\frac{5 \pi}{6}\right\} \) \( \left\{\frac{5 \pi}{6}, \frac{11 \pi}{6}\right\} \) \( \left\{\frac{\pi}{6}\right\} \)
Trigonometry Jun 06, 2023
Solve the equation over the interval \( [0,2 \pi) \). \[ \tan x=-\frac{\sqrt{3}}{3} \] \[ \left\{\frac{\pi}{6}, \frac{7 \pi}{6}\right\} \] \( \left\{\frac{5 \pi}{6}\right\} \) \( \left\{\frac{5 \pi}{6}, \frac{11 \pi}{6}\right\} \) \( \left\{\frac{\pi}{6}\right\} \)
Trigonometry Jun 06, 2023
Use the given information to find the exact function value. Given \( \sin \theta=\frac{1}{9} \) and \( \tan \theta>0 \), find \( \cos 2 \theta \)
Trigonometry Jun 06, 2023
Use the given information to find the exact function value. Given \( \sin \theta=\frac{1}{9} \) and \( \tan \theta>0 \), find \( \cos 2 \theta \). \( -\frac{8 \sqrt{5}}{9} \) \( \frac{79}{81} \) \( -\frac{79}{81} \) \( \frac{8 \sqrt{5}}{9} \)
Trigonometry Jun 06, 2023
Use the given information to find the exact function value. Given \( \cos \theta=-\frac{\sqrt{5}}{5} \) and \( \sin \theta>0 \), find \( \sin 2 \theta \) \( -\frac{2}{5} \) \( \frac{2}{5} \) \( \frac{4}{5} \) \( -\frac{4}{5} \)
Trigonometry Jun 06, 2023
Use the given information to find the exact function value. Given \( \csc \theta=\frac{17}{8} \) and \( \cos \theta>0 \), find \( \tan 2 \theta \) \( \frac{240}{161} \) \( \frac{240}{289} \) \( -\frac{240}{161} \) \( -\frac{240}{289} \)
Trigonometry Jun 06, 2023
Use the given information to find the exact function value. Given \( \sec \theta=\frac{13}{5} \) and \( \theta \) is in quadrant IV, find \( \cos 2 \theta \) \( -\frac{119}{169} \) \( \frac{120}{169} \) \( \frac{119}{169} \) \( -\frac{120}{169} \)
Trigonometry Jun 06, 2023
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