Takes arccos (inverse cosine) ofx. The answer will be in radians. acos (x) Let T

Question

Takes arccos (inverse cosine) ofx. The answer will be in radians. acos (x) Let To) be the linear transformation that rotates any vector in R' through an angle ei in a right-handed sense about the axis (so if your right points along the positive xi-axis. is the direction that your fingers curl. It will have matrix 1 0 0 [T (0) 0 coso, Sin 0, 0 sin cost, An important property of this transformation is that it leaves any vector parallel to the xi-axis unchanged, as you would expect. You can easily check this by confirming that By way of contrast, any vector v lying in the x2x-plane (the plane whose equation can be written xi-0) is rotated through the angle 0 while remaining in the rzrs-plane. To see this define the vector v whose components are given by the column matrix: D

Explanation / Answer

Dear Student Thank you for using Chegg !! Transformation Matrix corresponding to rotation about x axis by an angle A is given by T (A) = 1 0 0 0 Cos A -SinA 0 Sin A Cos A Given A = pi/3 T (pi/3) = 1 0 0 0 0.5 -0.86603 0 0.866025 0.5 Transformation Matrix corresponding to rotation about z axis by an angle B is given by T(B) = Cos B -Sin B 0 Sin B Cos B 0 0 0 1 Given B = pi/4 T (pi/4) = 0.707107 -0.70711 0 0.707107 0.707107 0 0 0 1 Now transformation matrix of first rotation about z axis by pi/4 and then about x axis by pi/3 T (pi/4) * T(pi/3) = 0.707107 -0.70711 0 0.353553 0.353553 -0.86603 0.612372 0.612372 0.5 Solution

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