The vector between (-5, 2) and (-7, 9) represented in <em>trigonometric</em> form is described by the expression 7.280 · (cos 105.945° i + sin 105.945° j).
<h3>How to determine a vector in polar form</h3>
Let be a vector in <em>rectangular</em> form, that is, a vector of the form <em>(x, y)</em>. A vector in <em>polar</em> (<em>trigonometric</em>) form is defined by the following expression: <em>(r, θ)</em>
And the magnitude (<em>r</em>) and direction of the vector (<em>θ</em>), in degrees, are, respectively:
<h3>Magnitude</h3>
(1)
<h3>Direction</h3>
![\theta = \tan^{-1}\frac{y}{x}](https://tex.z-dn.net/?f=%5Ctheta%20%3D%20%5Ctan%5E%7B-1%7D%5Cfrac%7By%7D%7Bx%7D)
And the vector in rectangular form is described below:
<em>(x,y) = (-7, 9) - (-5, 2)</em>
<em>(x,y) = (-2, 7)</em>
And its polar form is determined below:
![r = \sqrt{(-2)^{2}+7^{2}}](https://tex.z-dn.net/?f=r%20%3D%20%5Csqrt%7B%28-2%29%5E%7B2%7D%2B7%5E%7B2%7D%7D)
![r = \sqrt{53}](https://tex.z-dn.net/?f=r%20%3D%20%5Csqrt%7B53%7D)
<em>r ≈ 7.280</em>
<em />
<em>θ = tan⁻¹ (-7/2)</em>
<em>θ ≈ 105.945°</em>
And the vector between (-5, 2) and (-7, 9) represented in <em>trigonometric</em> form is described by the expression 7.280 · (cos 105.945° i + sin 105.945° j). ![\blacksquare](https://tex.z-dn.net/?f=%5Cblacksquare)
To learn more on vectors, we kindly invite to check this verified question: brainly.com/question/13322477