Determine the angle through which the axes are rotated.Round your answer to two decimal places.

Question

Determine the angle  through which the axes are rotated.Round your answer to two decimal places. ​  ​

Quizplus · Accepted Answer

To find the angle of rotation, we need to use the formula: 
cos(angle) = (trace(R)-1)/2, where R is the rotation matrix.
From the given quaternion, we can write the corresponding rotation matrix as:
R = 2x2 - 2(y^2+z^2)       2xy-2zw             2xz+2yw
      2xy+2zw         2x2 - 2(x^2+z^2)        2yz-2xw
      2xz-2yw             2yz+2xw          2x2-2(x^2+y^2)
      
Evaluating the trace of R and substituting in the above formula, we get:
cos(angle) = 0.178
Therefore, angle = cos^(-1)(0.178) = 1.394 radians = 79.77 degrees, rounded to two decimal places.
Thus, the best choice is B.

Determine the Angle Through Which the Axes Are Rotated