Question 957063
use x for  θ 
Evaluate the expression under the given conditions. sin(x/2); tan x = &#8722; 3/4 , x in Quadrant IV (assume 0 < x < 2&#960;)
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working with a (3-4-5) reference right triangle in quadrant IV where sin<0, cos>0
cos x=4/5 (In Q4)
{{{sin(x/2)=sqrt((1-cos x)/2)=sqrt((1-(4/5))/2)=sqrt((1/5)/2)=sqrt(1/10)=sqrt(10)/10}}}

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Check: w/calculator
tanx=-3/4(In Q4)
x=323.13
x/2=161.57
sin(x/2)=sin(161.57)&#8776;0.3162
Exact value=&#8730;10/10&#8776;0.3162