https://file.aiquickdraw.com/mathbot/file/172971024196570xu7c92.jpg

The point \((9, 74^\circ)\) represents a polar coordinate, where 9 is the radius and \(74^\circ\) is the angle. In polar coordinates, angles can be expressed in different forms by adding or subtracting multiples of \(360^\circ\) (since the angles repeat every full rotation). 

We are looking for equivalent points in the image where the radius is 9 and the angle is equivalent to \(74^\circ\) by adding or subtracting \(360^\circ\). This gives us:

\[
74^\circ + 360^\circ = 434^\circ
\]
\[
74^\circ - 360^\circ = -286^\circ
\]

Thus, \((9, 74^\circ)\) is equivalent to both \((9, 434^\circ)\) and \((9, -286^\circ)\). These two points appear in the image.

So, the points in the image that are equivalent to \((9, 74^\circ)\) are:

- \((9, 434^\circ)\)
- \((9, -286^\circ)\)

Would you like more details on how polar coordinates work or have any questions about this? Here are some related questions:

1. How are angles in polar coordinates calculated and adjusted?
2. How can we convert polar coordinates to Cartesian coordinates?
3. What happens when the radius is negative in polar coordinates?
4. How would you find the distance between two points in polar coordinates?
5. Can multiple angles describe the same point in polar coordinates?

**Tip:** In polar coordinates, a point can have multiple equivalent representations by changing the angle by \(360^\circ\) or multiples of it!

Learn how to find the equivalent points for the polar coordinate (9, 74°) by adjusting the angle by multiples of 360°. This solution involves key concepts in polar coordinates and periodic functions, making it suitable for high school students in Grades 10-12.

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