The vertical displacement ddd (in mm) of a tuning fork's prong over a cycle is modeled by the function
d=sinθ∘ d = \sin \theta^\circ d=sinθ∘for −360≤θ≤360-360 \le \theta \le 360−360≤θ≤360.
A point A A\,A on the displacement curve has coordinates (a,−32)(a, -\frac{\sqrt{3}}{2})(a,−23).
(i) Determine the value of aaa, given that −180<a<−90-180 < a < -90−180<a<−90.
(ii) State the value of sin(a∘+720∘)\sin(a^\circ + 720^\circ)sin(a∘+720∘).
A second point B B\,B on the curve has coordinates (b,37)(b, \frac{3}{7})(b,73), where 0<b<900 < b < 900<b<90.
(i) Find the exact value of sin(b∘−180∘)\sin(b^\circ - 180^\circ)sin(b∘−180∘).
(ii) Find the exact value of cosb∘\cos b^\circcosb∘.
