Question

The vector v has magnitude 17 and makes an angle of 105 with the positive x direction.
Express v in terms of components, with i and j being unit vectors pointing in the positive x and y directions.

Answer 1

v = 17(cos105, sin105)
= 17cos105 i - 17sin105 j

since 105 = 60+45 degrees, and thus one of the "special" angles, they probably want exact values
cos105 = cos(60+45)
= cos60cos45 - sin60sin45
= (1/2)(√2/2) - (√3/2)(√2/2)
= (√2 - √6)/4

sin105 = sin(60+45)
= sin60cos45 + cos60sin45
= (√3/2)(√2/2) + (1/2)(√2/2)
= (√6 + √2)/4

v = (17/4)(√2-√6) i - (17/4)(√2 + √6) j