If sin (x) =2/5 and tan(x) > 0, what is sin(2x)?

Answer:

sin2x = [tex]\frac{4\sqrt{21} }{25}[/tex]

Step-by-step explanation:

Given sinx = [tex]\frac{2}{5}[/tex] = [tex]\frac{opposite}{hypotenuse}[/tex]

Then the third side, the adjacent is found using Pythagoras' identity, that is

adj² + opp² = hyp²

adj² + 2² = 5²

adj² + 4 = 25 ( subtract 4 from both sides )

adj² = 21 ( take the square root of both sides )

adj = [tex]\sqrt{21}[/tex] , then

cosx = [tex]\frac{adj}{hyp}[/tex] = [tex]\frac{\sqrt{21} }{5}[/tex]

Using the double angle identity

sin2x = 2sinxcosx

         = 2 × [tex]\frac{2}{5}[/tex] × [tex]\frac{\sqrt{21} }{5}[/tex]

         = [tex]\frac{4\sqrt{21} }{25}[/tex]

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vende 3/5 del total del terreno y recibe por
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​

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