A ball attached to a spring is raised 2 feet and released with an initial vertical velocity of 3 feet per second. The distance of the ball from its rest position after t seconds is given by d = 2 cos t + 3 sin t. Show that 2cost + 3sin t =√13 cos(t - θ), where θ lies in quadrant I and tan θ = 3/2. Use the identity to find the amplitude and the period of the ball’s motion.

Trigonometry (MindTap Course List)
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ISBN:9781337278461
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Chapter3: Additional Topics In Trigonometry
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A ball attached to a spring is raised 2 feet and released with an initial vertical velocity of 3 feet per second. The distance of the ball from its rest position after t seconds is given by d = 2 cos t + 3 sin t.

Show that 2cost + 3sin t =√13 cos(t - θ), where θ lies in quadrant I and tan θ = 3/2. Use the identity to find the amplitude and the period of the ball’s motion.

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