SOLUTION: The previous question was written incorrectly. It should read: Use the half-angle formulas to determine the exact values of sinx, cosx, and tanx given {{{ -17(pi)/12 }}}

Question 814433: The previous question was written incorrectly. It should read:
Use the half-angle formulas to determine the exact values of sinx, cosx, and tanx given
Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
Use the half-angle formulas to determine the exact values of sinx, cosx, and tanx given: -17π/12
***
-17π/12=(-17π/6)/2
-17π/6=(-2π-5π/6)=210˚
sin(210˚)-1/2
cos(210˚)=-√3/2
tan(210˚)=√3/3
..
Identity: sin(x/2)=�√((1-cos(x))/2)
sin(-17π/6)/2)=√((1+√3/2)/2)=√((2+√3)/4)
..
Identity: cos(x/2)=�√((1+cos(x))/2)
cos(-17π/6)/2)=-√((1-√3/2)/2)=-√((2-√3)/4)
..
Identity: tan(x/2)=(sin(x))/(1+cos(x))
tan(-17π/6)=-(1/2)/(1-(√3/2))=-1/(2-√3)
..
calculator check:
..
sin(-17π/12)≈0.9659..
exact value as computed=√((2+√3)/4)≈0.9659..
..
cos(-17π/12)≈-0.2588..
exact value as computed=-√((2-√3)/4)≈0.2588..
..
tan(-17π/12)≈-3.732..
exact value as computed=-1/(2-√3)≈-3.732..
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