Inverse with trig

[Guest]

f(x)=cos(2x) 0<=x<= pi/2 a=1

find inv of f(a) for the function and the given real number a

is the inverse of cos (2x)= x/cos 2? If not, how do I find the inverse of cos

Thanks

 

[tkhunny]

is the inverse of cos (2x)= x/cos 2?

Ummm...no. The right hand side is a line! How could that be the inverse of the cosine?

Usually, the inverse cosine is called the "invese cosine" or "arccosine". You must define it and restrict the Domain of the cosine so it's inverse is a function. If you've never done it, it coule be a struggle. What do you know about the cosine function, reflection across the line x = y, and the nature of a function? You will need to know all that to accomplish your task. It is not an algebra problem.

 

[Guest]

What I know about cosine across the line x=y. It intersects with x=y at (1,1). Also, the graph of cos(2x) never goes below the x axis.

 

[tkhunny]

\(\displaystyle cos(2*(\frac{\pi}{2})) = cos(\pi) = -1\)

This seems to indicate you have not been prepared properly to solve this problem.