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Answer :

Answer:

D.   -[tex]\sqrt{17}[/tex]/8

Step-by-step explanation:

Draw a right triangle such that cos (theta) = 8/9.  That means the hypotenuse = 9 and the adjacent side to theta = 8

Use the Pythagorean theorem to find the opposite side to theta

[tex]\sqrt{9^{2} - 8^{2} } = \sqrt{81 - 64} = \sqrt{17}[/tex]

tan (theta) = [tex]\sqrt{17}[/tex]/8

Since theta is in quadrant IV, the tan is negative.  So, tan (theta) = -[tex]\sqrt{17}[/tex]/8

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After considering the equation. Assuming  8 is an angle in quadrant iv, the value of tan(Ф) is:√17/8

Value of tan(Ф)

Given:

Equation=cos(Ф)=8/9

Using pythagorean theorem formula

H²=P²+B²

Where:

B=8

H=9

Let plug in the formula

P²=9²-8²

P=√81-64

P=√17

Since 8 is an angle in quadrant iv. Hence:

Value of TanФ=√17/8

Inconclusion the value of tan(Ф) is:√17/8

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