$\"\"$

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(a)

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The function is $\"\"$ .

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

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$\"\"$

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$\"\"$ .

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To find the slope $\"\"$ of the tangent line at $\"\"$ , evaluate $\"\"$ .

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

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$\"\"$

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$\"\"$ .

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The slope of the tangent line of function $\"\"$ is $\"\"$ .

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Number of complete cycles in the interval $\"\"$ is $\"\"$ .

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$\"\"$

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(b)

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The function is $\"\"$ .

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

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$\"\"$

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$\"\"$ .

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To find the slope $\"\"$ of the tangent line at $\"\"$ , evaluate $\"\"$ .

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$\"\"$

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$\"\"$ .

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The slope of the tangent line of function $\"\"$ is $\"\"$ .

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Number of complete cycles in the interval $\"\"$ is $\"\"$

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The slope of the tangent line of $\"\"$ at the origin is $\"\"$ .

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$\"\"$

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(a) The slope of the tangent line of function $\"\"$ is $\"\"$ .

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(b) The slope of the tangent line of function $\"\"$ is $\"\"$ .

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The slope of the tangent line of $\"\"$ at the origin is $\"\"$ .