x=3sinu
How can I write 1/3 sec u in terms of x?
So if I am understanding correctly, you want to write
in terms of x where you use the equation
Well, we know that , thus
We also know the mother of all identities is which can be solved for as
Now, using the equation do you think you can finish this?
Actually, the " ± " is justified. The cosine function (and thus the secant function) can have the same or opposite sign as the sine function, depending upon the quadrant.
Also, when Soroban found that , he found it by taking the square root of , so it should have been , if you prefer to look at it this way.