Quadratic Mathematics Assessment

Question 1 Let n be a positive integer of at least 2. Then,

1. for even n, sin" x may be expressed as the sum of cos(kx),

2. for odd n, sin" x may be expressed as the sum of sin(kx), and

3. for any n, cos" x may be expressed as the sum of cos(kx) where k is some of {1, 2, ..., n}.

(a) Verify the three statements above for n= 3, 4, 5 and 6. Use cos x = ? (eix +e-ix) and sin x = "-e(b) Use the relevant result from (a) and trigonometric identitities to calculate the exact value of sin x given that cos(2x) = 21

Question 2 Find the fourth roots of -8-8V3i. State them in polar form. Finally, sketch all on one complex plane.