Mathematics: The cartesian coordinates of a point in the xy plane are x = −5.25 m, y = −2.21 m. find the distance r from the point to the origin. answer in units of m. calculate the angle θ between the radius-vector of the point and the positive x axis (measured counterclockwise from the positive x axis, within the limits of −180◦ to +180◦)

25+25+25+10+10. The bar and the weights weigh 95 pounds....

The cartesian coordinates of a point in the xy plane

lovelyheart5337

15.03.2022

r = 5.696 and θ = 157.17°.

Step-by-step explanation:

the point is (-5.25,-2.21). The distance from the point to the origin is calculated with the formula

$r = \sqrt{x^{2}+y^{2}} = \sqrt{(-5.25)^{2}+(-2.21)^{2}} = \sqrt{27.56+4.88} = \sqrt{32.44}$

r = 5.696 m.

I drew the point and the distances in the plane. to find te angle we can use the sin formula:

sin(θ) = $\frac{2.21}{r} = \frac{2.21}{5.696} = 0.388$

θ = $sin^{-1}(0.388)= 22.83$ .

within the range of -180° and 180° the angle will be θ = 180-22.83 = -157.17°

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