Find the component form of the vector that has the given magnitude and direction angle Θ. ‖𝐯‖ = 5 and Θ = 315⁰.

Answer 1

the angle is the same as -45 degrees 360-315 =45 degrees is the reference angle

the coordinates of the point with magnitude 5 and angle 315 are the sides of a right triangle, each length = 5/sqr2 = 5/1.414 = 3.54 rounded to 2 decimal places

the point (3.54, -3.54)

Answer 2

the angle is the same as -45 degrees 360-315 =45 degrees is the reference angle

the coordinates of the point with magnitude 5 and angle 315 are the sides of a right triangle, each length = 5/sqr2 = 5/1.414 = 3.54 rounded to 2 decimal places

the point (3.54, -3.54)

Answer 3

component form in terms of x and y:

v_x = ||v||cos(theta) = 5cos(315^o) = 3.53

v_y = ||v||sin(theta) = 5sin(315^o) = -3.53

(v_x, v_y) = (3.53, -3.53)