SOLUTION: 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)

Algebra ->  Trigonometry-basics -> SOLUTION: 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)      Log On


   

Question 929908: 1 - A certain angle satisfies cos(x) = -3/4, pi a) cos(2x)
b) sin(x/2)
c) tan(x/2)
Answer by lwsshak3(11628) About Me  (Show Source):
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1 - A certain angle satisfies cos(x) = -3/4, pi 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=-√(1-cos^2(x))=-√(1-(9/16))=-√(7/16)=-√7/4
..
a) cos(2x)=cos^2(x)-sin^2(x)=9/16-7/16=2/16=1/8
b) sin(x/2)=
c) tan(x/2)=sinx/(1+cosx)=