Solving an equation involving sin and cos terms

[nokia8650]

Hi

I was wondering if there is a non-numericla way to solve the following equation:

144 - 90sin x - 155.8cos x = 0

Thanks

 

[HallsofIvy]

Hi

I was wondering if there is a non-numericla way to solve the following equation:

144 - 90sin x - 155.8cos x = 0

Thanks

That's not a nice equation but here's what I might do: write it as 90 sin x= 144- 155.8 cos x
$90\sqrt{1- cos^2 x}= 144- 155.8 cos x$ and square both sides to get $8100(1- cos^2 x)= 20736- 44870.4cos x+ 24273.64cos^2 x$. Solve that quadratic equation for cos x and then take the arccosine to find x. When you square both sides of an equation, that new equation may have roots that do not satisfy the original equation.

 

[nokia8650]

Thank you!