$\"\"$

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(a)

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The general form of cosine function is $\"\"$ .

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where, $\"\"$ is amplitude, $\"\"$ is the period and $\"\"$ is the shift along $\"\"$ -axis.

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Observe the graph. The difference between the maximum height and the minimum height is twice of the amplitude of the function.

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$\"\"$

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$\"\"$

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$\"\"$ .

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The amplitude of the function is $\"\"$ .

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Period of the function is $\"\"$ .

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The cosine function completes one half of the cycle between the times at maximum height and minimum height.

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$\"\"$ .

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$\"\"$

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$\"\"$ .

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Phase shift along $\"\"$ -axis is the time where maximum height occurs.

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The time at maximum height is $\"image\"$ .

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$\"\"$

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$\"\"$

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Since midline $\"\"$ ,hence $\"\"$

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Substitute $\"\"$ , $\"\"$ and $\"\"$ and $\"\"$ in $\"\"$ .

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$\"\"$

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Therefore,the function is $\"\"$ .

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$\"\"$

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(b)

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Rewrite the function $\"\"$ as a sine function.

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The general form of sine function is $\"\"$ .

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Observe the graph:

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The amplitude of the function is $\"\"$ and $\"\"$ .

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The function has a phase shift of $\"\"$ units to left.

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Therefore, $\"\"$ and $\"\"$ .

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Substitute all the values in $\"\"$ .

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Therefore,The function is $\"\"$ .

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$\"\"$

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(c)

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Rewrite $\"\"$ as a cosine function of a single angle.

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The function is $\"\"$ .

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$\"\"$

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(d)

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The function is $\"\"$ .

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Find all solutions of $\"\"$ .

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$\"\"$

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$\"\"$

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The general solutions for $\"\"$ is $\"\"$ .

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The solutions of $\"\"$ is $\"\"$ .

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$\"\"$

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(e).

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The general function is $\"\"$ .

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Where $\"\"$ is the phase shift around the $\"\"$ -axis.

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observe the graph:

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There is no pahse shift around the $\"\"$ -axis.

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Hence, the value of the $\"\"$ is $\"\"$ .

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$\"\"$

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(a)The function is $\"\"$ .

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(b) The function is $\"\"$ .

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(c) The function is $\"\"$ .

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(d) The solutions of $\"\"$ is $\"\"$ .

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(e) There is no pahse shift around the $\"\"$ -axis.Hence, the value of the $\"\"$ is $\"\"$ .