Question

If tanx=-3/4, 3π/2<x<2π,then find sin2x...​

Answer 1

~ Trigonometry

Hi There ! Hope this can help you :

$\tan(x) = \frac{y}{x} = - \frac{3}{4}$

find the value of z :

$z = \sqrt{ {x}^{2} + {y}^{2} } \\ z = \sqrt{ {4}^{2} + {3}^{2} } \\ z = 5$

Hence , we got :

$\sin(2x) = 2 \cos(x) . \sin(x) \\ \sin(2x) = 2 \: . \: \frac{x}{y} \: . \: \frac{y}{z} \\ \sin(2x) = 2 \: . \: \frac{4}{5} \: . \: \frac{3}{5} \\ \sin(2x) = \frac{24}{25}$

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