Answer the following questions related to the symmetry of trigonometric functions:
a. (i) Show that sin(180∘−θ)=sinθ for any real angle θ.
b. (ii) Show that cos(180∘−θ)=−cosθ for any real angle θ.
c. (iii) Explain, with reference to the signs of the coordinates of a point on the unit circle, why the results obtained in (i) and (ii) agree with the fact that sine is positive and cosine is negative in the second quadrant.