What are the x and y components of a vector a in the xy plane if its direction is 285° counterclockwise?

Question

from the positive direction of the x axis and its magnitude is 6.9 m?

Answer 1

Counterclockwise is the conventional rotational direction and the +x direction is the conventional starting direction for measuring such angles. The x component will be 6.9 cos 285° and the y component will be 6.9 sin 285°. If your calculator doesn't understand this, you can convert to an angle between 0 and 90 degrees by using a few trigonometric identities. If trig () is any of the common trigonometric functions, then

trig (a - 360°) = trig (a)

For specific trig functions,

cos (-a) = cos (a)
sin (-a) = -sin (a)

Answer 2

285 deg counterclockwise puts it in the fourth quadrant.

360 - 285 = 75

A = SQRT(6.9) (cos(75)i - sin(75)k)

where i is the unit vector in x directions and k is the unit vector in the y direction

A = 1.786i - 6.665k