$\"\"$

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The trigonometric expression is $\"\"$ .

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$\"italic$ , let $\"begin$ and place $\"begin$ in quadrant III.

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The point P = (x, y) = (12, 5) is on a circle of radius, $\"\"$ .

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$\"\"$ (Substitute $\"\"$ )

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$\"Syntax$ (Simplify)

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$\"begin$ (Simplify)

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$\"begin$ (Simplify)

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$\"italic$ (Substitute y = 5, r = 13)

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$\"italic$ (Substitute x = 12, r = 13) $\"\"$

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$\"\"$ , let $\"begin$ and place $\"begin$ in quadrant III.

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The point P = (x, y) = $\"begin$ = x < 0 is on a circle of radius, $\"begin$ .

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$\"Syntax$ (Substitute $\"\"$ )

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$\"Syntax$ (Simplify)

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$\"Syntax$ (Subtract 1 from each side)

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$\"Syntax$ (Simplify)

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$\"x$ (x < 0)

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$\"italic$ (Substitute $\"x$ , r = 2)

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$\"italic$ $\"\"$

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a) $\"italic$

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The sum formula for the sine function: $\"italic$ .

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Substitute $\"\"$ .

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$\"\"$

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$\"\"$ (Simplify)

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$\"\"$ (Rewrite the expression with common denominator)

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The value of $\"italic$ $\"equal$ . $\"\"$

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b) $\"italic$

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The sum formula for the sine function: $\"italic$ .

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Substitute $\"\"$ .

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$\"Syntax$

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$\"equal$

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$\"equal$ (Simplify)

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The value of $\"\"$ $\"equal$ . $\"\"$

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c) $\"\"$

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The difference formula for the sine function: $\"italic$ .

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Substitute $\"\"$

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$\"Syntax$

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$\"equal$ (Simplify)

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$\"equal$ (Rewrite the expression with common denominator)

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The value of $\"\"$ $\"equal$ . $\"\"$

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The difference formula for the tangent function: $\"italic$ .

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

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$\"equal$

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$\"equal$ (Simplify)

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$\"equal$ (Simplify)

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The value of $\"italic$ $\"equal$ .

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$\"\"$

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The solution is

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(a) The value of $\"italic$ $\"equal$ .

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(b) The value of $\"\"$ $\"equal$ .

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(c) The value of $\"\"$ $\"equal$ .

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(d) The value of $\"italic$ $\"equal$ .