Given Sec(x)= 3/2 with 3pi/2 < x < 2pi, find sin (x/2).

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1 Answer

sec(x)=3/2, then cos(x)=⅔ in quadrant 4, as requested.

When x is between 3π/2 and 2π, x/2 is between 3π/4 and π, so sin(x/2) is positive.

cos(x)=2cos2(x/2)-1, cos2(x/2)=½(cos(x)+1)=⅚. sin(x/2)=√(1-⅚)=√⅙ or √6/6.

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