A rotational sensor records that the cosine of an angle turned by a wheel is 0.65.
a. (i) Calculate the principal value α=arccos(0.65) correct to three decimal places (radians).
b. (ii) Convert α to degrees, correct to one decimal place.
c. (iii) Within the interval 0≤θ≤2π, determine all values of θ that satisfy cosθ=0.65. Give each value in radians correct to three decimal places and briefly justify your selections based on the symmetry of the cosine function and principal value considerations.