SOLUTION: Find the exact value of csc(-17π / 12)

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Question 913871: Find the exact value of csc(-17π / 12)
Answer by lwsshak3(11628) About Me  (Show Source):
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Find the exact value of csc(-17pi / 12)
csc%28-17pi%2F12%29=%281%2Fsin%28-17pi%2F12%29%29
sin(-17pi/12)
=-sin(17pi/12)
=-sin(8pi/12+9pi/12)
=-sin(2pi/3+3pi/4)
=-sin(120˚+135˚)
=-(sin120cos135+cos120sin135)
=-(√3/2*-√2/2+(-1/2)(√2/2)
=-(-√6/4+(-√2/4)=(√6+√2)/4
sin(-17pi/12)=(√6+√2)/4
csc(-17pi/12)=4/(√6+√2)
Check:(using sin)
sin(-17pi/12)≈0.9659
exact value=(√6+√2)/4≈0.9659