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Find sin(2x), cos(2x), and tan(2x) from the given information. sec(x) = 4, x in Quadrant IV

sin(2x) =

cos(2x) =

tan(2x) =

Hello Guest!

$sin(2x)=2sin(x)cos(x)=2\frac{\pm \sqrt{sec^2(x)-1}}{sec(x)}\times\frac{1}{sec(4)}\\ sin(2x) =2\frac{-\sqrt{4^2-1}}{4}\times\frac{1}{4}\\$

$sin(2x)_{sec(x)=4}=-0.4841$

$cos(2x)=2cos^2(x)-1=2\times \frac{1}{sec^2(x)}-1\\ cos(2x)=2\times \frac{1}{4^2}-1\\$

$cos(2x)_{sec(x)=4}=-0.875$

$tan(2x)=\frac{2tan(x)}{1-tan^2(x)}=\frac{2\cdot (\pm\sqrt{sec^2(x)-1})}{1-(sec^2(x)-1)}$

$tan(2x)=\frac{2\times (-\sqrt{4^2-1})}{1-(4^2-1)}$

$tan(2x)_{sec(x)=4}=0.55328$

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