Question 1032544
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If ∠A is ACUTE and cos A = 4/5 find sin A, cos 2A, sin 2A, and tan 2A 
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1.  sin(A) = {{{sqrt(1-cos^2(A))}}} = {{{sqrt(1-(4/5)^2)}}} = {{{sqrt(1-16/25)}}} = {{{sqrt((25-16)/25)}}} = {{{sqrt(9/25)}}} = + {{{3/5}}} = {{{3/5}}}.

    Notice that the sign is "+" for sine, because &#8736;A is ACUTE.


2.  cos(2A) = {{{cos^2(A) - sin^2(A)}}} = {{{(4/5)^2}}} - {{{(3/5)^2}}} = {{{(16-9)/25}}} = {{{7/25}}}.


3.  sin(2A) = 2*sin(A)*cos(A) = {{{2*(3/5)*(4/5)}}} = {{{24/25}}}.


4.  tan(2A) = {{{sin(2A)/cos(2A)}}} = {{{(24/25):(7/25)}}} = {{{24/7}}} = {{{3}}}{{{3/7}}}.
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