Find the exact value of s in [0,π) and cos s=-1/2

Let α=−83π /9 [a]  Find the reference angle for α . Show all work in radians, not degrees. [b]  Find four angles between 0 and 2π with the same reference angle as α . Show all work in radians, not degrees. [c]  Which of the four angles in part [b] have negative cosecant values ? Justify your answer using the definition of cosecant, not ASTC.

Let B= {1, cost, cos?t, ., cos °t} and C={1, cost, cos 2t, ... , cos 6t). Assume the following trigonometric identities. cos 2t = - 1+2 cos ?t cos 3t = - 3 cos t+ 4 cos t cos 41 = 1-8 cos?t+8 cos t cos 5t = 5 cost- 20 cos t+ 16 cos St cos 61 = - 1+ 18 cos?t- 48 cos "t+ 32 cos °t Let H be the subspace of functions spanned by the functions in B. Then B is a basis for H. Complete parts (a) and (b). a. Write the B-coordinate vectors of the vectors in C as the columns of a matrix P, and use them to show that C is a linearly independent set in H. P =