Find the acute angle of rotation a that eliminates the xy term. State approximate solution to the nearest 0.1 .
A)76.7 °
B)13.3 °
C)9.2 °
D)67.5 °
E)22.5 °

Question

Find the acute angle of rotation a that eliminates the xy term. State approximate solution to the nearest 0.1 . 
A)76.7 ° 
B)13.3 ° 
C)9.2 ° 
D)67.5 ° 
E)22.5 °

Quizplus · Accepted Answer

To eliminate the xy term, we need to rotate the coordinate system such that the line y=x gets aligned with one of the coordinate axes. This can be achieved by rotating the original coordinate system by an angle of 45 degrees (pi/4 radians) clockwise or counterclockwise. Since we want the acute angle of rotation, we choose the smaller angle which is 45-22.5=22.5 degrees, or pi/8 radians, counterclockwise. Therefore, the answer is D) 67.5 degrees.

Find the Acute Angle of Rotation a That Eliminates the Xy