Answer:
The composition of two rotations is additive by concatenation.
Step-by-step explanation:
Let's consider two rotations, R(theta1) and R(theta2) where theta1 and theta2 are the angles of rotation in degrees. The composition of the two rotations is given by:
R(theta2) o R(theta1)
The above expression means first rotate by an angle of theta1, and then rotate the resulting position by an angle of theta2. We can represent this composition of two rotations as a matrix multiplication:
cos(theta2) -sin(theta2) 0 * cos(theta1) -sin(theta1) 0
sin(theta2) cos(theta2) 0 sin(theta1) cos(theta1) 0
0 0 1 0 0 1
Simplifying the above matrix multiplication, we get:
cos(theta1 + theta2) -sin(theta1 + theta2) 0
sin(theta1 + theta2) cos(theta1 + theta2) 0
0 0 1
This means that the composition of two rotations by concatenation is equivalent to a single rotation of angle (theta1 + theta2). Therefore, the composition of two rotations is additive by concatenation.