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 cos ( x ) + b sin ( 2 x )
to give x = f ( y )?
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Answers (1)

Amaya Vance
Answered 2022-10-26 Author has 6 answers
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 [ π 2 , π 2 ]
In your function f ( x ) = a cos x + b sin 2 x, the domain is R , and it's a periodic function, so it clearly does not have an inverse function. The same goes with g ( x ) = a sin x + b sin 2 x
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