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Chapter 6: Problem 21

A point in rectangular coordinates is given. Convert the point to polar coordinates. $$(-3,4)$$

Short Answer

Expert verified
The polar coordinates equivalent of the rectangular coordinates (-3, 4) are approximately (5, 126.87掳) or in radians (5, 蟺 + arctan(4/-3)).

Step by step solution

01

Calculate r - the radius

Use the formula \(r = \sqrt{x^2 + y^2}\) to calculate the radius r. So \(r = \sqrt{(-3)^2 + 4^2} = \sqrt{9 + 16} = \sqrt{25} = 5\).
02

Calculate 胃 - the angle

Use the formula \(\theta = \arctan(y/x)\) to calculate the angle in radians. However, because x is negative and y is positive, this point lies in the second quadrant. So we need to add 蟺 to the result of the arctan function. We get \(\theta = \arctan(4/-3) + \pi\).
03

Convert 胃 to degrees

If you prefer to express 胃 in degrees, remember that 蟺 radians is equivalent to 180 degrees. By calculating, we get \(\theta \approx 126.87 degrees\).

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Most popular questions from this chapter

In Exercises 73-78, solve the trigonometric equation. $$ \sqrt{2} \sec \theta=2 \csc \frac{\pi}{4} $$

\(r=3+6 \sin \theta\)

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