ALL vectors have two components (x and y) To determine the components, sketch an arrow with the head in the general direction described – at the tail of the arrow, draw in the angle if there is one Calculate the amount of the arrow that points in the x-direction and the amount that points in the y-direction (be sure to include the sign; use trig if there is an angle) 22 X = - 22 Y = 0.0
Remember that the angle is ALWAYS AT THE TAIL OF THE VECTOR and is ALWAYS TOUCHING THE DIRECTION STATED SECOND (so, this angle is touching east) 85 opp 24° adj Draw in components (dashed arrows pointing in the directions given) The components are ALWAYS drawn SUCH THAT THE ANGLE GIVEN IS IN THE RIGHT TRIANGLE Label opp and adj and solve → adj 85 cos(24) = 77.7 85 sin(24) = 34.6 X = + 77.7 Y = + 34.6 → opp
55 X = 0.0 Y = + 55
110 cos(30) = 95.3 → adj 110 sin(30) = 55 → opp X = - 55 Y = - 95.3 30° adj opp 110 cos(30) = 95.3 110 sin(30) = 55 → adj X = - 55 Y = - 95.3 → opp
→ adj 42 cos(50) = 27.0 42 sin(50) = 32.2 → opp X = - 32.2 Y = + 27.0 50° → adj 42 cos(50) = 27.0 42 sin(50) = 32.2 → opp X = - 32.2 Y = + 27.0
→ adj 75 cos(30) = 65.0 75 sin(30) = 37.5 → opp X = + 37.5 Y = - 65.0 30° 75 adj opp 75 cos(30) = 65.0 75 sin(30) = 37.5 → adj → opp X = + 37.5 Y = - 65.0