Question

Solve for the exact solutions in the interval [0, 27). If the equation has no solutions, respond with DNE. cse?(x) = Preview Points possible: 10

Answer 1

Given csť (X) = , [0, 21) cse (): CSC(X) = + 2 V3 cse(x) = 2 x= CSc "(26) CSC(x) = 715 I 31; The corecant function is positive in the first and second quadrants. To find the second solution, subtract. The reference angle from it to find the solution in the second quadrant. 24- T-TES .

x=2" The period of the asc (²) function is sol values will repeat every att radians in both directions (x= I +21th, 2I +2 17h, for any integern CSC (X) = -23 x = cact (-2 ) x = -1 - The corecant function is negative in the third and fourth quadrant. To find the second 'solution Subtract the volution - from at to find a reference angle Next add this reference angle to IT to find the solution in the third quadrant 2= 25--) + - 25++ x = 4th

- Add 24 to every negative argle to get positive angles. xa-T + 2017 x=51 The period of the CSC(2) function is 2T so values will repeat every at radians in both directions. x= 4T + 270, ST / +2950, for any integer n. - Plug in i for n. and simplify to see if the solution is contained in [0, 27) (x= 25., sa