How do you find the exact value of the sin, cos, and tan of the angle -105 degrees?

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Answer 1 · 2018-07-30T03:47:00

Below

$sin(-105)$

$=sin(-60-45)$

$=sin((-60)+(-45))$

$=sin(-60)cos(-45)+cos(-60)sin(-45)$

$=-sqrt3/2timessqrt2/2+1/2times-sqrt2/2$

$=-sqrt6/4-sqrt2/4$

$=(-sqrt6-sqrt2)/4$

$cos(-105)$

$=cos(-60-45)$

$=cos((-60)+(-45))$

$=cos(-60)cos(-45)-sin(-60)sin(-45)$

$=1/2timessqrt2/2-(-sqrt3/2times-sqrt2/2)$

$=sqrt2/4-sqrt6/4$

$=(sqrt2-sqrt6)/4$

$tan(-105)$

$=tan(-60-45)$

$=tan((-60)+(-45))$

$=(tan(-60)+tan(-45))/(1-tan(-60)tan(-45)$

$=(-sqrt3-1)/(1-(-sqrt3)(-1))$

$=(-sqrt3-1)/(1-sqrt3)$

$=(-(sqrt3+1))/(1-sqrt3)$

$=(sqrt3+1)/(sqrt3-1)$