Given cos A= 2/5 for those value for A below, what is sin (A/2)?

#cos A=2/5 ......... (3(pi))/(2) < A <2pi#

1 Answer
Jim G.
Feb 22, 2018

#sin(A/2)=+sqrt30/10#

Explanation:

#"using the "color(blue)"half angle formula"#

#color(red)(bar(ul(|color(white)(2/2)color(black)(sin(A/2)=+-sqrt((1-cosA)/2))color(white)(2/2)|)))#

#"since "(3pi)/2< A<2pi" then A is in the fourth quadrant"#

#"where "sinA<0#

#rArr(3pi)/4 < A/2< pi#

#rArrsin(A/2)=+sqrt((1-2/5)/2)#

#color(white)(rArrsin(A/2))=+sqrt(3/10)=+sqrt3/sqrt10=+sqrt30/10#

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