Find the coordinates of the point at $1426^{\circ}$ on a circle of radius 2.9 centered at the origin.
Round your answers to three decimal places.

Step 1 ：The problem is asking for the coordinates of a point on a circle after rotating 1426 degrees around the origin. The circle is centered at the origin and has a radius of 2.9.

Step 2 ：We know that the coordinates of a point on a circle can be found using the formulas \(x = r \cos(\theta)\) and \(y = r \sin(\theta)\), where \(r\) is the radius of the circle and \(\theta\) is the angle of rotation in radians.

Step 3 ：However, the angle given in the question is in degrees, so we need to convert it to radians first. We can do this using the formula \(\theta_{\text{radians}} = \theta_{\text{degrees}} \times \frac{\pi}{180}\).

Step 4 ：Also, since a full rotation around a circle is 360 degrees, we can simplify the problem by finding the equivalent angle within 360 degrees. This can be done by taking the remainder when dividing the angle by 360.

Step 5 ：Let's calculate these values. The radius is 2.9 and the angle in degrees is 1426. The angle in radians is approximately 6.03883921190038.

Step 6 ：Using the formulas for the coordinates of a point on a circle, we find that \(x = 2.814\) and \(y = -0.702\).

Step 7 ：\(\boxed{\text{Final Answer: The coordinates of the point at } 1426^\circ \text{ on a circle of radius 2.9 centered at the origin are } (2.814, -0.702)}\)