Harmon Bates
05/27/2024 · Junior High School
A clock face is attached to a tower so that its centre is 60 m above the ground. The hour hand is 2 m in length and starts out pointing at 3 on the clock face. a) Sketch a graph that represents the height of the tip of the hour hand relative to the angle it forms with the horizontal as it rotates for 1 day. b) Determine an equation that represents the height of the tip of the hour hand with respect to the ground. c) How would the graph and equation change if the hour hand were 3 m in length? d) How would the graph and equation change if the hour hand had started out pointing at the 9 on the clock face?
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a) Sketch a graph with the height of the tip of the hour hand as a function of the angle it forms with the horizontal, using the equation \( h = 60 + 2 \sin(\theta) \).
b) The equation is \( h = 60 + 2 \sin(\theta) \).
c) If the hour hand is 3 m in length, the equation becomes \( h = 60 + 3 \sin(\theta) \).
d) If the hour hand starts at 9, the equation becomes \( h = 60 + 2 \sin(\theta - 90) \).
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