# Solving Inverse Function: sec(2x+180)=2, 0<x<360

In summary, The conversation is discussing how to solve the equation sec(2x+180)=2, with a given range of 0<x<360. The suggestion is to change it to cos(2x+180)=1/2 and then get rid of the 180, but this would not result in the correct answers for x. Another suggestion is to change the cosine to -cos(2x) = 1/2 or set the argument of the cosine as it stands to the values that have cosine = 1/2 within the specified interval.
I can only find two answers for this equation, whereas the books says it should be four. Can someone enlighten me? Showing the procedure would help:P

(degrees)
sec(2x+180) = 2 0<x<360

First write it as cos(2x+180)=1/2.

Then get rid of the 180 (the 180 causes a shift in the graph of cos(2x)).

Galileo said:
First write it as cos(2x+180)=1/2.

Then get rid of the 180 (the 180 causes a shift in the graph of cos(2x)).

Changing to cosine is a good idea, but you can't get rid of 180 and get the right answers for x. You could change the cosine to -cos(2x) = 1/2, or set the argument of the cosine as it stands to the values that have cosine = 1/2, then solve for x, keeping only the solutions in the specified interval.

OlderDan said:
You could change the cosine to -cos(2x) = 1/2
That's what I meant by 'getting rid of the 180'.

Check the range of x:
0 < x < 360
180 < 2x + 180 < 900

## 1. What is an inverse function?

An inverse function is a function that "undoes" the action of another function. In other words, given a function f(x), the inverse function would return the value of x that was originally input into f(x). In mathematical notation, the inverse function is denoted as f^-1(x).

## 2. How do you solve inverse functions?

To solve inverse functions, you can use the following steps:
1. Rewrite the equation in the form of f(x) = y.
2. Switch the x and y variables.
3. Solve for y.
4. Replace y with f^-1(x) to get the final inverse function.

## 3. What is the inverse of the secant function?

The inverse of the secant function is the cosine function, cos(x). This means that if you input a value into the cosine function, the output will be the angle whose secant is equal to that value.