$\"\"$

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a.

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The trigonometric equation is $\"\"$ .

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Rewrite the equation as $\"\"$

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Apply sine difference identity : $\"\"$ .

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$\"\"$

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Solve $\"\"$ in the interval $\"\"$ .

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$\"\"$

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The general solution of $\"\"$ is $\"\"$ , where $\"image\"$ is an integer.

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The solution is $\"\"$ , where $\"image\"$ is an integer.

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If $\"\"$ , $\"\"$ .

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If $\"\"$ , $\"\"$ .

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If $\"\"$ , $\"\"$ .

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Thus, the solutions are $\"\"$ , $\"\"$ , and $\"\"$ on the interval $\"\"$ .

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$\"\"$

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b.

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The trigonometric equation is $\"\"$ .

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Let the functions are $\"\"$ and $\"\"$ .

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Draw a coordinate plane.

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Graph the two functions $\"\"$ and $\"\"$ on the interval $\"\"$ in same window.

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Graph :

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$\"\"$

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Observe the above graph :

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The two functions intersects at $\"\"$ , $\"\"$ , and $\"\"$ on the interval $\"\"$ . $\"\"$

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a. The solutions are $\"\"$ , $\"\"$ , and $\"\"$ on the interval $\"\"$ .

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b. The two functions intersects at $\"\"$ , $\"\"$ , and $\"\"$ on the interval $\"\"$ .