$\"\"$

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The trochoid equations are $\"\"$ and $\"\"$ .

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(a) Find the slope of the tangent line.

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$\"\"$

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

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$\"\"$

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$\"\"$ .

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$\"\"$

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

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$\"\"$

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$\"\"$ .

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Slope of the tangent line is $\"\"$ .

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$\"\"$ .

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Substitute $\"\"$ and $\"\"$ .

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$\"\"$ .

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

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$\"\"$

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(b)

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The vertical tangent line occurs when $\"\"$ .

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$\"\"$

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$\"\"$

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The cosine function lies between $\"\"$ .

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if $\"\"$ , then $\"\"$ is never zero.

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Therefore, there is no vertical tangent line.

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$\"\"$

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

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(b) $\"\"$ , no vertical tangent line.