Given that tanx = 8 and sinx is positive, determine sin(2x), cos(2x), and tan(2x). Write the exact answer. Do not round.

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03-11-2022
Mathematics

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Given that tanx = 8 and sinx is positive, determine sin(2x), cos(2x), and tan(2x). Write the exact answer. Do not round.

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AmreenO87990 AmreenO87990 · Answer 1 · 2022-11-03T23:34:41-04:00

[tex]\begin{gathered} \tan x=8 \\ x=\tan ^{-1}_{}(8) \\ x=82.87^0 \end{gathered}[/tex][tex]\begin{gathered} \sin (2x)=\sin 2(82.87) \\ \Rightarrow\sin (165.74) \\ \Rightarrow\sin (2x)=0.25 \end{gathered}[/tex][tex]\begin{gathered} \cos (2x)=\text{cos}2(82.87) \\ \Rightarrow\cos (165.74) \\ \Rightarrow\cos (2x)=-0.97 \end{gathered}[/tex][tex]\begin{gathered} \tan (2x)=\tan 2(82.87) \\ \Rightarrow\tan (165.74) \\ \Rightarrow\tan (2x)=-0.25 \end{gathered}[/tex]

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