Question 596062: using the half angle formulas how do i find the exact value of the sin,cos,tan for (7/12)pi, i just dont understand trig at all
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! using the half angle formulas how do i find the exact value of the sin,cos,tan for (7/12)pi, i just dont understand trig at all.
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(7π/6)=2*(7π/12
or
(7π/6)/2=(7π/12)
using half-angle formulas
..
sin(7π/12)=sin(7π/6)/2)=±√[(1-cos(7π/6)/2]
select + root because 7π/12 is in quadrant II where sin>0
=√[(1-cos(7π/6)/2]
=√[(1+√3/2/2]
=√[(2+√3)/4]
..
cos(7π/12)=cos(7π/6)/2)=±√[(1+cos(7π/6)/2]
select - root because 7π/12 is in quadrant II where cos<0
=-√[(1+cos(7π/6)/2]
=-√[(1-√3/2)/2]
=-√[(2-√3)/4]
..
tan(7π/12)=tan(7π/6)/2
=sin (7π/6)/(1+cos((7π/6)
=(-1/2)/(1-√3/2)
=-1/(2-√3)
multiply top and bottom by (2+√3)
=-(2+√3)/4-3
=-(2+√3)
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