$\"\"$

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The function is $\"\"$ .

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Where $\"\"$ is angular displacement in radians, $\"\"$ is time in seconds.

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Find the maximum angular displacement.

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$\"\"$

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The cosine function ranges between $\"\"$ to $\"\"$ .

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$\"\"$ .

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$\"\"$ is maximum when $\"\"$ is maximum.

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The maximum value of $\"\"$ is $\"\"$ .

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The maximum angular displacement is $\"\"$ .

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$\"\"$

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Find the rate of change of $\"\"$ when $\"\"$ seconds.

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$\"\"$

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Apply derivative on each side with respect to $\"\"$ .

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$\"\"$

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Apply formula: $\"\"$ .

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$\"\"$

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$\"\"$

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Substitute $\"\"$ in above function.

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$\"\"$

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$\"\"$

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$\"\"$ .

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Rate of change of $\"\"$ when $\"\"$ is $\"\"$ rad/sec.

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$\"\"$

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The maximum angular displacement is $\"\"$ rad.

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Rate of change of $\"\"$ when $\"\"$ is $\"\"$ rad/sec.