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Chapter 6: Problem 102

The rectangular coordinates of a point are given. Use a graphing utility in radian mode to find polar coordinates of each point to three decimal places. $$(-4.308,-7.529)$$

Short Answer

Expert verified
The polar coordinates of the point (-4.308,-7.529) to three decimal places are \( (8.680, -2.104) \)

Step by step solution

01

- Calculate the Radius \( r \)

The radius \( r \) is calculated using the Pythagorean theorem from the x and y coordinates. The equation is \( r = \sqrt{(x^2 + y^2)} \). By substituting the given values into the equation, we will get the radius to three decimal places.
02

- Calculate the Angle

The angle \( \theta \) in radian mode can be calculated using the tangent function: \( \theta = \arctan\left(-\frac{y}{x}\right) \) for x < 0. Using the provided x and y values from the coordinates and substitifying them into this equation will give us the polar angle to three decimal places.
03

- Final Polar Coordinates

Now that we have calculated both the radius \( r \) and the angle \( \theta \), we can express the given point in polar coordinates. The polar coordinates are often expressed as \( (r, \theta) \).

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