Solve 5/2cos2x-1/2=3sinx to two decimal places where x is equal or between 0 and 2pi

Question

p0sitr0n · Answer

expand cos2x and pair it up with sinx to get tanx and then check where the solution is located on the function

anonymous · Answer

can you rewrite your question in equation, so it will be more clear?

anonymous · Answer

the equation is $$\frac{ 5 }{ 2 }\cos^2x-\frac{ 1 }{ 2 }=3sinx$$

anonymous · Answer

@mihirb  ok

solomonzelman · Answer

Oh, have you ever heard of this?
$$sinx=\sqrt{1-Cos^2x}~~~~~~~~~~and$$$$cosx=\sqrt{1-Sin^2x}$$

solomonzelman · Answer

Good tip no?

solomonzelman · Answer

$$5Cos^2x-1=6Sinx$$$$5(\sqrt{1-Sin^2x})-1=6Sinx~~~~~~~~l et~~Sinx=a$$

solomonzelman · Answer

$$5\sqrt{1-a^2}-1=6a,~~~~~add~~~1~~~t o~~~both~~~sides,$$$$5\sqrt{1-a^2}=6a+1~~~~~~~squa re~~~both~~~sides,$$$$25(1-a^2)=36a^2+12a+1~~~~~~->~~~~~25-25a^2=36a^2+12a+1~~~~->$$$$61a^2+12a+26~~~~solve~~for~~a~~and~~substitute~~the~~result~~into~~Sinx=a$$