Algebra-2

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

 

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.

 

Now, 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 3 units, and the horizontal line segment has a length of 4 units.

 

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

 

 

In this case, the opposite side is the length of the vertical line segment, which is 3 units, and the hypotenuse is the distance from the origin to the point . We can calculate the hypotenuse using the Pythagorean theorem:

 

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