Question

How do you evaluate csc(-22pi/6) - cot(19pi/7) + sec(-17pi/5)?

Answer 1

Evaluate trig functions.

Explanation:

1. csc x = 1/sin x. Find `sin ((-22pi)/6)`
   `sin ((-22pi)/6) = sin ((2pi)/6 - (24pi)/6) = sin (pi/3 - 4pi) =`
   = `sin (pi/3) = sqrt3/2.` Therefor,
   `csc ((-22pi)/6) = 2/sqrt3 = (2sqrt3)/3`
2. Use calculator to find `cot ((19pi)/7)`
   `cot ((19pi)/7) = cot ((5pi)/7 + (14pi)/7) = cot ((5pi)/7 + 2pi)`=
   `cot = (5pi)/7 = cot ((5(180))/7) = cot (128^@57)`
   cot 128.57 = - tan (128.57 + 180) = tan (-51.43)
   Calculator --> tan (-51.43) = -1.25
3. `sec = 1/cos`. Find `cos ((-17pi)/5)`
   `cos ((-17pi)/5) = cos ((3pi)/5 - (20pi)/5) = cos ((3pi)/5 - 4pi) =`
   `= cos ((3pi)/5) = cos 108^@`
   Calculator --> cos 108 = -0.31
   `sec ((-17pi)/5) = 1/-0.31 = -3.24`