Answer:
2) Midline: [tex]\displaystyle y = 1[/tex]
Amplitude: [tex]\displaystyle 2[/tex]
Period: [tex]\displaystyle 2\pi[/tex]
Horisontal Shift: [tex]\displaystyle \pi[/tex]
1) Midline: [tex]\displaystyle y = -2[/tex]
Amplitude: [tex]\displaystyle 1[/tex]
Period: [tex]\displaystyle \pi[/tex]
Horisontal Shift: [tex]\displaystyle 0[/tex]
Step-by-step explanation:
2) [tex]\displaystyle \boxed{y = 2cos\:(\theta - 1\frac{1}{2}\pi) + 1} \\ y = Acos\:(B\theta - C) + D \\ \\ Vertical\:Shift \hookrightarrow D \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \\ Amplitude \hookrightarrow |A| \\ \\ Vertical\:Shift \hookrightarrow 1 \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \hookrightarrow \boxed{1\frac{1}{2}\pi} \hookrightarrow \frac{1\frac{1}{2}\pi}{1} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \hookrightarrow \boxed{2\pi} = \frac{2}{1}\pi \\ Amplitude \hookrightarrow 2[/tex]
OR
[tex]\displaystyle y = Asin\:(B\theta - C) + D \\ \\ Vertical\:Shift \hookrightarrow D \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \\ Amplitude \hookrightarrow |A| \\ \\ Vertical\:Shift \hookrightarrow 1 \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \hookrightarrow \boxed{\pi} \hookrightarrow \frac{\pi}{1} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \hookrightarrow \boxed{2\pi}\hookrightarrow \frac{2}{1}\pi \\ Amplitude \hookrightarrow 2[/tex]
1) [tex]\displaystyle \boxed{y = sin\:(2\theta + \frac{\pi}{2}) - 2} \\ y = Asin\:(B\theta - C) + D \\ \\ Vertical\:Shift \hookrightarrow D \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \\ Amplitude \hookrightarrow |A| \\ \\ Vertical\:Shift \hookrightarrow -2 \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \hookrightarrow \boxed{-\frac{\pi}{4}} \hookrightarrow \frac{-\frac{\pi}{2}}{2} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \hookrightarrow \boxed{\pi} = \frac{2}{2}\pi \\ Amplitude \hookrightarrow 1[/tex]
OR
[tex]\displaystyle y = Acos\:(B\theta - C) + D \\ \\ Vertical\:Shift \hookrightarrow D \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \\ Amplitude \hookrightarrow |A| \\ \\ Vertical\:Shift \hookrightarrow -2 \\ Horisontal\:[Phase]\:Shift \hookrightarrow 0 \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \hookrightarrow \boxed{\pi}\hookrightarrow \frac{2}{2}\pi \\ Amplitude \hookrightarrow 1[/tex]
With the information above, you now should have an ideya of how to interpret trigonometric equations and graphs like these.
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