(a) For each of the following angles, reduce the given angle to its principal value lying in the interval 0≤θ<2π. Write the principal value clearly in terms of π.
(i) −611π (ii) −45π (iii) 623π (iv) −37π
(b) State in which quadrant the principal value of each angle obtained in part (a) lies.
(c) Using your answers to part (b), explain the sign (positive or negative) of sinθ, cosθ and tanθ for each of the four angles given in part (a). Give reasons for every sign you state.