(a) Define the principal value of an angle (in radians).
(b) State the principal value ranges generally adopted for evaluating (i) sine and cosine, and (ii) tangent.
(c) Explain why any real angle can be replaced by its principal value when one wishes to read the values of sine or cosine from the unit circle.
(d) Identify the quadrant in which the angle −230∘ lies and, without actual calculation, state the expected signs of sin(−230∘) and cos(−230∘), giving reasons.