Algebra-2

To determine the value of , we can use the given information that the terminal side of in standard position contains the point .

 

In standard position, the initial side of the angle is the positive x-axis, and the terminal side is the line segment that forms the angle with the positive x-axis. Since the terminal side passes through the point , it forms a right triangle with the x-axis and the vertical line segment from the origin to the terminal side.

 

Let's consider the right triangle formed by the terminal side, the x-axis, and the vertical line segment from the origin to the terminal side. The vertical line segment has a length of 4 units, and the horizontal line segment has a length of 3 units.

 

Using the definition of secant in a right triangle, we have:

 

 

In this case, the hypotenuse is the distance from the origin to the point , which we can calculate using the Pythagorean theorem:

 

Click "Show Answer" to reveal the answer and analysis