4sinx - 3cosx = 0 is given. Find sin2x.

Question

kashmoneyjr · Answer

Too lazy to solve it by myself lol, but heres my take:
Add 3cosx to each side
4sinx=3cosx
divide each side by cosx to get 4(sinx/cosx)=3
divide each side by 4 to get sinx/cosx=3/4
sinx/cosx=tanx, so tanx=3/4
x=inversetan(3/4) (which im too lazy to calculate)
then calculate sin2x, using the value you found

elifbestegul · Answer

Thank you but I was not looking for an answer which would need to be calculated on a calculator. Thanks anyway @kashmoneyjr

kashmoneyjr · Answer

Thats a tough question then
you probably already know this, but using the identity sin2x=2sinxcosx may help

elifbestegul · Answer

yes, it needs to be done with that formula but I can't figure out how to @kashmoneyjr

irishboy123 · Answer

$4 \sin x = 3 \cos x $

irishboy123 · Answer

$\tan x = \dfrac{3}{4}$

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kashmoneyjr · Answer

^this: use the 3-4-5 triangle

kashmoneyjr · Answer

if tanx=3/4, then by the right triangle definition, sinx=3/5 and cosx=4/5
so sin2x=2sinxcosx=2*(3/5)*(4/5)

kashmoneyjr · Answer

so 24/25

irishboy123 · Answer

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