Answer:
15/12, which simplifies to 5/4
Explanation:
In order to determine the value of sec Theta, we need to find the length of the hypotenuse of the right triangle formed by dropping a vertical line from the x-axis to the point (12, -9).
To do this, we can use the Pythagorean theorem, which states that the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.
In this case, the length of the vertical side is 9 (since the point is 9 units below the x-axis), and the length of the horizontal side is 12 (since the point is 12 units to the right of the y-axis).
So, the square of the length of the hypotenuse is equal to 9^2 + 12^2 = 81 + 144 = 225.
Therefore, the length of the hypotenuse is the square root of 225, which is 15.
Finally, we can use the definition of secant, which is equal to the hypotenuse divided by the adjacent side (in this case, the adjacent side is 12), to find the value of sec Theta.
So, sec Theta is equal to 15/12, which simplifies to 5/4.
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