A rotational sensor records that the cosine of an angle turned by a wheel is .
MATHEMATICS · Multi-part · AP · AP Precalculus · Trigonometric and Polar Functions · Trigonometric and Polar Functions
Problem
A rotational sensor records that the cosine of an angle turned by a wheel is 0.65.
(i) Calculate the principal value α=arccos(0.65) correct to three decimal places (radians).
(ii) Convert α to degrees, correct to one decimal place.
(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.