Hi, my teacher sent me this question. He says to show work, but i dont know how to show the work. thx

Question

csc minus (31pie/6) equals.....

Answer 1

csc(-31pi/6)

= 1/sin(-31pi/6) = 1/sin(36pi/6 - 31pi/6) add or subtract any integer multiple 2pi and the trig functions are the same. 6pi=36pi/6 =3(2pi)

=1/sin(5/6 pi)

5/6 pi is almost 180 degrees. 5pi/6 = 150 degrees. The sine of 150 degrees is 1/2

csc(-31pi/6) = 1/sin(150 degrees) = 1/1/2 = 2

csc(-31pi/6) = 2