Suppose that A is an acute angle and cosA=4/5. Find the exact value of sinA/2 ?

1 Answer
Jim G.
Apr 26, 2018

#sin(A/2)=sqrt10/10#

Explanation:

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

#•color(white)(x)sin(A/2)=+-sqrt((1-cosA)/2)#

#"since A is an acute angle then "sin(A/2)>0#

#sin(A/2)=+sqrt((1-4/5)/2)+sqrt((1/5)/2)=+sqrt(1/10)#

#color(white)(xxxxxx)=1/sqrt10=sqrt10/10#

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