the particle undergoes 2 displacements, measured from the positive x-axis, with

Question

the particle undergoes 2 displacements, measured from the positive x-axis, with counterclockwise positive. The first has magnitude of 11m and makes an angle of 66 degrees. with positive x axis. The resultant displacement has magnitude of 6.3m directed atan angle of 130 degrees from the positive x-axis.
I found the magnitude of the second vector it is 9.99659m, the answer is correct.
then I need to find the angle of hte second displacement (measured from the positive x axis, with counterclockwise positive and within the limits -180 to +180) answer in degrees.

Explanation / Answer

first displacement s = 11 cos 66*i + 11 sin 66 j = 4.474 i +10.04 j resultant displacment S = 6.3 cos 130 i + 6.3 sin 130 j = -4.049 i +4.826 j so, second displacment s ' = S - s = -4.049 i +4.826 j -4.474 i-10.04 j = - 8.523i -5.213 j magnitude of second displacment s ' = sqrt [ -8.523^2+-5.213^2] = 9.99m let the s' makes an angle theta with negative x-axis then tan (theta) = 5.213 / 8.523 theta = 31.45 degrees angle with positive x-axis = 180 + theta = 211.45 degrees counterclockwise

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