I was able to solve a similar question finding the roots of the tan(x) function with a transformation, but this one seems to be giving me a bit more trouble...

The equation is y = 2sec(-2x + 180) + 3

I know to find the roots I have to set y to 0 and solve for x.

This is what I've done so far:

y = 2sec(-2x + 180) + 3

0 = 2sec (-2x + 180) + 3

-3 = 2sec (-2x + 180)

-3/2 = sec (-2x + 180)

sec^-1 (-3/2) = -2x + 180

This is where I'm running into trouble. I know that sec = 1/cos, so I rewrote this line as:

1/(cos^-1 (-3/2) ) = -2x + 180

But I'm not able to solve for cos^-1 (-3/2) so now I'm at a bit of a loss.

Any help would be greatly appreciated. Thanks so much!!!