$\"\"$

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Position of the horse after $\"\"$ seconds can be modeled by $\"\"$ .

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Where

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$\"\"$ : time in seconds.

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$\"\"$ : phase shift.

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Compare the above equation with $\"\"$ .

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Here $\"\"$ and $\"\"$ .

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Period $\"\"$

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$\"\"$

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Period is $\"\"$ .

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Here period is $\"\"$ the function reaches a maximum height at $\"\"$ radians.

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Phase shift is the difference between the horizontal positions of the function at $\"\"$ and $\"\"$ .

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$\"\"$

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Therefore phase shift is $\"\"$ .

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Phase shift $\"\"$ .

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$\"\"$

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Substitute $\"\"$ in $\"\"$ .

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Thus, the equation is $\"\"$ . $\"\"$

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The equation is $\"\"$ .