# Can anyone invert y=a cos(x)+b sin(2x) to give x=f(y)?

Chaim Ferguson 2022-10-25 Answered
Can anyone invert
$y=a\mathrm{cos}\left(x\right)+b\mathrm{sin}\left(2x\right)$
to give $x=f\left(y\right)$?
You can still ask an expert for help

• Live experts 24/7
• Questions are typically answered in as fast as 30 minutes
• Personalized clear answers

Solve your problem for the price of one coffee

• Math expert for every subject
• Pay only if we can solve it

Amaya Vance
Notice that the inverse trigonometric functions are not actually the inverse of trigonometric functions. For example, sinx doesn't actually have an inverse as it fails the horizontal line test. The inverse only exists when we restrict sinx's domain to be $\left[-\frac{\pi }{2},\frac{\pi }{2}\right]$
In your function $f\left(x\right)=a\mathrm{cos}x+b\mathrm{sin}2x$, the domain is $\mathbb{R}$, and it's a periodic function, so it clearly does not have an inverse function. The same goes with $g\left(x\right)=a\mathrm{sin}x+b\mathrm{sin}2x$