Question 445214
We know by our double angle formulas that {{{sin(2theta) = 2sin(theta)cos(theta)}}}
We are given that {{{cos(theta) = 3/5}}} So construct a triangle with adjacent side 3 and hypotenuse 5. Then following the Pythagorean Theorem, the opposite side of {{{theta}}} is 4.
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Thus, {{{sin(theta) = 4/5}}}
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So, {{{sin(2theta) = 2*(4/5)*(3/5) = highlight(24/25)}}}