Question

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

Answer 1

`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`