Floyd Davison
09/16/2024 · Senior High School
Given this transformed cosine function \( y=\cos \left(\frac{1}{2}(\theta-\pi)\right)+7 \)
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The transformed cosine function \( y=\cos \left(\frac{1}{2}(\theta-\pi)\right)+7 \) is horizontally shifted right by \( \pi \) units, compressed horizontally by a factor of 2, and shifted up by 7 units. The amplitude is 1, the period is \( 4\pi \), the phase shift is \( \pi \) to the right, and the vertical shift is 7 units. The range is \([6, 8]\), and there are no x-intercepts. The maximum value is 8 and the minimum value is 6.
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