Question

Vector u has an initial point at (−5, 2) and a terminal point at (−7, 9). Which of the following represents u in trigonometric form?
u = 7.28(cos 74.055°i + sin 74.055j)
u = 7.28(cos 105.945°i + sin 105.945°j)
u = 7.28(sin 74.055°i + cos 74.055°j)
u = 7.28(sin 105.945°i + cos 105.945°j)

Answer 1

The vector between (-5, 2) and (-7, 9) represented in trigonometric form is described by the expression 7.280 · (cos 105.945° i + sin 105.945° j).

How to determine a vector in polar form

Let be a vector in rectangular form, that is, a vector of the form (x, y). A vector in polar (trigonometric) form is defined by the following expression: (r, θ)

And the magnitude (r) and direction of the vector (θ), in degrees, are, respectively:

Magnitude

$r = \sqrt{x^{2}+y^{2}}$     (1)

Direction

$\theta = \tan^{-1}\frac{y}{x}$

And the vector in rectangular form is described below:

(x,y) = (-7, 9) - (-5, 2)

(x,y) = (-2, 7)

And its polar form is determined below:

$r = \sqrt{(-2)^{2}+7^{2}}$

$r = \sqrt{53}$

r ≈ 7.280

θ = tan⁻¹ (-7/2)

θ ≈ 105.945°

And the vector between (-5, 2) and (-7, 9) represented in trigonometric form is described by the expression 7.280 · (cos 105.945° i + sin 105.945° j). $\blacksquare$

To learn more on vectors, we kindly invite to check this verified question: brainly.com/question/13322477