Question 1040562
.
Find sin2x from the given information.

sinx=-(3/5)


x in Quadrant III
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Use this formula of Trigonometry

sin(2x) = 2*sin(x)*cos(x).

You just know that sin(x) = {{{-3/5}}} (it is given).

Based on it, you can calculate

cos(x) = -{{{sqrt(1 - sin^2(x))}}} = -{{{sqrt(1 -(-3/5)^2)}}} = -{{{sqrt(1-9/25)}}} = -{{{sqrt((25-9)/25)}}} = -{{{sqrt(16/25)}}} = -{{{4/5}}}.

Notice that the sign before the square root is negative, since the function cosine is negative for x in Q3.

Now you are on the finish line to calculate sin(2x):

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

<U>Answer</U>.  sin(2x) = {{{24/25}}}.
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