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)
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)
5
(2 stars)
3
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
Direction
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 ≈ 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).
To learn more on vectors, we kindly invite to check this verified question: https://brainacademy.pro/question/13322477