Mathematics

Problem

Let

E = \sin 1000^{\circ} + \cos(-740^{\circ}) + \tan 2490^{\circ}

. (a) Reduce the angles

1000^{\circ},\,-740^{\circ}

and

2490^{\circ}

to suitable principal values for evaluating sine, cosine and tangent respectively. (b) Determine the exact value of each trigonometric term. (c) Hence find the exact value of

E

. (d) For each of the three given angles, mention the quadrant in which its principal value lies and comment on the sign you obtained for the corresponding trigonometric ratio.

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