what point if equivalent to (1,20°) in polar coordinate?&nbsp;

Question

what point if equivalent to (1,20°) in polar coordinate?&amp;nbsp;

Don Sumner · Accepted Answer

To convert the point (1, 20°) from Cartesian coordinates to polar coordinates, we use the following formulas:

r = \sqrt{x^{2} + y^{2}}

θ = \arctan (\frac{y}{x})

where

r

represents the distance from the origin to the point, and

θ

represents the angle between the positive x-axis and the line connecting the origin and the point.
In this case, we are given the point (1, 20°), where

x = 1

and

y = 20 °

.
Let's calculate the values using these formulas:

r = \sqrt{1^{2} + 20 °^{2}} = \sqrt{1 + 400} = \sqrt{401}

θ = \arctan (\frac{20 °}{1}) = \arctan (20 °)

However, it's important to note that the arctan function typically returns angles in radians rather than degrees. To convert from radians to degrees, we can use the formula:

angle in degrees = angle in radians \times (\frac{180 °}{π})

Substituting the values, we have:

θ = \arctan (20 °) \times (\frac{180 °}{π})

Calculating the numerical value, we find:

θ \approx 86.415 °

Therefore, the point (1, 20°) in polar coordinates is approximately

(\sqrt{401}, 86.415 °)

.

what point if equivalent to (1,20°) in polar

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