Question 929908
1 - A certain angle satisfies cos(x) = -3/4, pi<x<3pi/2 Obtain, without a calculator,
a) cos(2x)
b) sin(x/2)
c) tan(x/2)
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reference angle x is in quadrant III where cos<0, sin<0
cosx=-3/4
sinx=-&#8730;(1-cos^2(x))=-&#8730;(1-(9/16))=-&#8730;(7/16)=-&#8730;7/4

..
a) cos(2x)=cos^2(x)-sin^2(x)=9/16-7/16=2/16=1/8
b) sin(x/2)={{{sqrt((1-cosx)/2)=sqrt((1+(3/4)/2))=sqrt((7/4)/2)=sqrt(7/8))}}}
c) tan(x/2)=sinx/(1+cosx)={{{(-sqrt(7)/4)/(1-(3/4))
=(-sqrt(7)/4)/(1/4)=-sqrt(7))}}}