Mathematics: If tan(x)=3/5 and sin(x) 0, what is sin(2x)? With STEPS PLEASE AND NO TROLLING.

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If tan(x)=3/5 and sin(x) 0, what is sin(2x)? With

sarahmkey6

05.02.2022

sin2x = $\frac{30}{34}$

Step-by-step explanation:

Given

tanx = $\frac{3}{5}$ = $\frac{opposite}{adjacent}$

This is a right triangle with legs 3 and 5

Let the hypotenuse be h , then using Pythagoras' identity

h² = 3² + 5² = 9 + 25 = 34 ( take the square root of both sides )

h = $\sqrt{34}$

Thus

sinx = $\frac{opposite}{hypotenuse}$ = $\frac{3}{\sqrt{34} }$

cosx = $\frac{adjacent}{hypotenuse}$ = $\frac{5}{\sqrt{34} }$

Hence

sin2x = 2sinxcosx = 2 × $\frac{3}{\sqrt{34} }$ × $\frac{5}{\sqrt{34} }$ = $\frac{2(3)(5)}{\sqrt{34}(\sqrt{34}) }$ = $\frac{30}{34}$

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