Question 1171118
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If and sin(a)=4/5, and "a" is an acute angle, find the exact value of sin 2a.
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If sin(a) = {{{4/5}}},  then cos(a) = {{{sqrt(1-sin^2(a))}}} = {{{sqrt(1-(4/5)^2)}}} = {{{sqrt((25-16)/25)}}} = {{{sqrt(9/25)}}} = {{{3/5}}}.


and we use the positive value of the square root, since the angle "a" is acute.


Next,  sin(2a) = one of the basic formula of Trigonometry = 2*sin(a)*cos(a) = {{{2*(4/5)*(3/5)}}} = {{{24/25}}}.    <U>ANSWER</U>
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Solved.