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

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Answer 1 · 2015-12-02T16:57:51

Evaluate trig functions.

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,
$csc ((-22pi)/6) = 2/sqrt3 = (2sqrt3)/3$
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
$sec = 1/cos$ . 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
$sec ((-17pi)/5) = 1/-0.31 = -3.24$